Here you can find some of my articles that got published in various Mathematical Magazines. This collection is being constantly updated as more publications come out, so please stay tuned!

    Publications » Mathematical Olympiads Group »

  1. !Inequality with log.PNG
  2. 1012. Sol...pdf
  3. 1021. Sol..pdf
  4. 1022. Sol..pdf
  5. 1023. Sol..pdf
  6. 1026.Sol..pdf
  7. 1036,1037,1038-Solutions..pdf
  8. 1037. Sol..pdf
  9. 1038. Sol..pdf
  10. 1041. Sol..pdf
  11. 1076.Sol..PNG
  12. 1079.Sol..PNG
  13. 1080.Sol..PNG
  14. 12038. Sol..pdf
  15. 12057(a) Sol..pdf
  16. 2580,2581,2585. Sol..pdf
  17. 3123, 3125-solutions.pdf
  18. 3167. CRUX v.33,n.6. Official solution..PNG
  19. 3167. Solution by proposer..PNG
  20. 3329.Solution by proposer..pdf
  21. 3719. Sol..pdf
  22. 3729. Sol..pdf
  23. 3941,3942 CRUX vol.40,n.5.PNG
  24. 3946. Two inequalities with internal angle bisectors.PNG
  25. 3948. Crux v.40,n.5 -Solution.PNG
  26. 3961. Sol..pdf
  27. 3964. Sol..pdf
  28. 3965. Sol..pdf
  29. 3970. Sol..pdf
  30. 4013. Official solutions..pdf
  31. 4103. Sol..pdf
  32. 4103.Sol..pdf
  33. 4158.Sol..pdf
  34. 4207. Proposed by Mihaela Berindeanu..PNG
  35. 4306. Solution..pdf
  36. 4308.Sol.pdf
  37. 4348. Sol..pdf
  38. 4491. Sol..pdf
  39. 4493. Sol..pdf
  40. 5211-official solutions 11.-2012.pdf
  41. 5335. Official solutions..pdf
  42. 5338. Solution by proposer..pdf
  43. 5358. Solution by proposer..PNG
  44. 5359. Three official solutions.pdf
  45. 5387. Official solutions.pdf
  46. 5398. Sol.pdf
  47. 5400. Solution by proposer.pdf
  48. 5404. Four official solutions..pdf
  49. 5453. Official solutions..pdf
  50. 5453. Sol..pdf
  51. 5466._Three official solutions-SSMA (January 2018).pdf
  52. 5467._Four official solutions (SSMA-January 2018).pdf
  53. 5477. Official solutions..pdf
  54. 5478. Official solutions..pdf
  55. 5478. Sol..pdf
  56. 5495. Official solutions..pdf
  57. 5495. Solution.(And one more limit of Lalescu kind sequence.).pdf
  58. 5519. Solution.pdf
  59. 5525-official solutions..pdf
  60. 866. Sol..pdf
  61. 936. Solution...pdf
  62. A Class of Inequalities_n.1.PNG
  63. A Class of Inequalities_n.2(short solution).PNG
  64. A Class of Inequalities_n.2.PNG
  65. A Class of Inequalities_n.3(J258).Sol..PNG
  66. A Class of Inequalities_n.4(S289). Sol..PNG
  67. A point P in the plane of a triangle.pdf
  68. A point P on the circumcircle of a right-angled triangle.pdf
  69. A trigonometric inequality.pdf
  70. AM-GM inequality with logarithms.pdf
  71. About natural numbers which is a sum of at least two consecutive naturals..PNG
  72. About one inequality with exp. function.PNG
  73. About one inequality. Its proofs and short history.pdf
  74. About one non linear recurrence of the third order.pdf
  75. About polynomials of degree 3.pdf
  76. About two properties of Fibonacci Numbers.pdf
  77. Additions to one problem (calculations of two integrals).pdf
  78. After translation..PNG
  79. Algebraic equivalent of Walker's Inequality..PNG
  80. Algebraic equivalent of one geometric inequality in acute triangle..PNG
  81. Algebraic inequality with geometric interpretation 2..PNG
  82. Algebraic inequality with geometric interpretation..PNG
  83. Algebraic inequality with geometric interpretation3.PNG
  84. Algebraic inequality with trigometric variations..pdf
  85. Algebraic version of triangle inequality for side lengths of Median Triangle..pdf
  86. Almost Vieta's system of equations..PNG
  87. Almost asymptotic inequality.PNG
  88. Alternating infinite sum with double factorial..pdf
  89. An inequality from IMO 2009 Shortlist from Estonia.pdf
  90. An inequality with radicals..pdf
  91. And again problem related to quadratically connected sequences..pdf
  92. And more pair of sequences that quadratically connected..PNG
  93. And one more limit related to e.pdf
  94. And without L'Hopital's Rule..PNG
  95. Angel's preserving linear mapping..pdf
  96. Another Cyclic inequality(corrected) ..PNG
  97. Another proof of inequality (1)..PNG
  98. Anti Reciprocal inequality..pdf
  99. Area of trapezoid(via partial areas).pdf
  100. Area via given partial areas..pdf
  101. Arithmetic progression defined by inequality.pdf
  102. Around main trigonometric identity in a triangle..pdf
  103. Asymmetric and nonhomogeneous inequality with three variables with square root..PNG
  104. Asymptotic behavior of one sequence defined recursively..PNG
  105. Asymptotic behavior of one sequence defined recursively..PNG
  106. Asymptotic of one sum..pdf
  107. Asymptotic representation of a sequence defined by non linear recurrence..PNG
  108. Asymptotic variant of the problem..PNG
  109. Basic inequalities with distances..pdf
  110. Basic inequality with distances..pdf
  111. Blundon's Inequality.pdf
  112. CRUX 1701-Solution.PNG
  113. Calculate limit with product of n differences..pdf
  114. Calculate the limit 2.pdf
  115. Calculate the limit 3.pdf
  116. Calculate the limit 4.pdf
  117. Calculate the limit 5.pdf
  118. Calculate the limit 6.pdf
  119. Calculate the limit 7.pdf
  120. Calculate the limit 8..pdf
  121. Calculate the limit 9..pdf
  122. Calculate the limit with binomomial coefficients.pdf
  123. Calculate the limit with hidden factorial.pdf
  124. Calculate the limit with power-exponential function..pdf
  125. Calculate the limit.PNG
  126. Calculate the limit.pdf
  127. Calculate the missing angle.pdf
  128. Calculation of one composite series..PNG
  129. Calculation of one infinite sum..pdf
  130. Calculation of one limit (without L'Hôpital's rule)..PNG
  131. Calculation of one limit by passing to limit under integral..PNG
  132. Calculation of the one limit with n-th root and ln.PNG
  133. Combined progression..PNG
  134. Compare the numbers(product of logarithms).pdf
  135. Compare two product with logarithms..PNG
  136. Compute the missing area..PNG
  137. Corrected statement of one problem.PNG
  138. Corrected statement of one problem_variant 1.PNG
  139. Corrected statement of one problem_variant 2.PNG
  140. Corrected variant of the problem..pdf
  141. Corrected version.PNG
  142. Correction to one limit problem..PNG
  143. Correlations between angles of two triangles with sides related by equations..PNG
  144. Counterexamples & correction.PNG
  145. Counterexamples & correction.pdf
  146. Criterion for existence of n-periodic orbits of one Mobius function.pdf
  147. Cyclic criterion for equilateral triangle..PNG
  148. Cyclic form of Schure's inequality(Solution with Wendy's Subst.).PNG
  149. Cyclic form of Schure's inequality..PNG
  150. Cyclic inequality from Indian TST to the IMO 2002.PNG
  151. Cyclic inequality in a triangle..PNG
  152. Cyclic inequality involving cube roots..PNG
  153. Cyclic inequality involving square roots.pdf
  154. Cyclic inequality with constraint..PNG
  155. Cyclic inequality with quadratic roots(variant2)..PNG
  156. Cyclic inequality with quadratic roots..pdf
  157. Cyclic inequality with three variable that belong to closed interval..PNG
  158. Cyclic inequality with three variables involving fractions..pdf
  159. Cyclic inequality.PNG
  160. Cyclic refinement of reciprocal inequality.pdf
  161. Decomposition of any natural number as sum of squares of rational numbers..pdf
  162. Definite integral involving sine, cosine and logarithm..PNG
  163. Definite integral with sine and cosine..PNG
  164. Difference representation of one binomial expansion.pdf
  165. Difference=perfect square..PNG
  166. Differential equation..PNG
  167. Divisibility by 40 of a natural numbers that satisfy two quadratic properties..PNG
  168. Divisibility property of a one sequence defined recursively.PNG
  169. Divisibility property of one sequence defined by nonlinear recurrence..PNG
  170. Double algebraic inequality with geometric interpretation of its right hand side..pdf
  171. Double inequality for ratio of double factorials..PNG
  172. Double inequality for variables that belong to a segment..PNG
  173. Double inequality for variables that belong to a segment..pdf
  174. Double inequality in N..pdf
  175. Double inequality related to Hyperfactorial.pdf
  176. Double inequality with GM and AM and involving ln..PNG
  177. Double inequality with constraint x+y+z=1..PNG
  178. Double inequality with side lengths, medians, inradius and circumradius..PNG
  179. Double inequality with sum of quadratic roots of consecutive natural numbers..PNG
  180. Double inequality with three variables and rational constraint..PNG
  181. Easy Inequality with n variables that on first glance looks scary..PNG
  182. Equation involving product of integer and fractional parts..PNG
  183. Equation with Fibonacci coefficients..pdf
  184. Equation with nested roots.png
  185. Evaluate infinite sum with tan..pdf
  186. Evaluation of one infinitely nested square roots..PNG
  187. Evalution of one limit..PNG
  188. Exact Trigonometric Product Mystery.PNG
  189. Existence of rational root between 1 and 2..PNG
  190. Exotic limit with e.PNG
  191. Explicit formula for sequence defined by nonlinear recurrence..PNG
  192. FQ_H840.pdf
  193. Find radius of the circle..PNG
  194. Find the minimum value....PNG
  195. Find the value of one cyclic expression.PNG
  196. Functional equation in continuous functions. (2).PNG
  197. Functional equation in polynomial functions..pdf
  198. Functional equation on N..pdf
  199. Functional equation with twice iterated function.pdf
  200. Functional equation.(U182).PNG
  201. Functional equation..PNG
  202. Generalization of 220. (Vu Duc Canh).PNG
  203. Generalization of Cyclic inequality from Indian TST to the IMO 2002.PNG
  204. Generalization of inequality involving sum with abs of differences..pdf
  205. Generalization of one limit..PNG
  206. Generation of all rational numbers in (0,1)..pdf
  207. Geometric Inequalities with polynomial 2xy+2yz+2zx2-sqr(x)-sqr(y)-sqr(z), v.22,n.2- 2014.pdf
  208. Geometric inequalities involving a,b,c,r,R.pdf
  209. Geometric inequality with maximal altitude..pdf
  210. Hard inequality.PNG
  211. Hard.pdf
  212. Hyperbola and Orthocenter Mystery..PNG
  213. Identity involving binomial coefficients with additions..pdf
  214. Identity with distances in equilateral triangle..PNG
  215. Identity with integer parts involving three square roots..PNG
  216. Identity with integer parts..PNG
  217. Identity with product of sines..pdf
  218. Identity with sum of binomial coefficients.pdf
  219. Identity with sum that involve binomial coefficients..PNG
  220. Identity(Two sums with integer parts)..pdf
  221. Inequalities with powers of binomials 1+x,1-x.PNG
  222. Inequalities with two variables Cut the Knot.pdf
  223. Inequality for a sequence defined by recurrence.PNG
  224. Inequality for acute tringle with tan and sec..PNG
  225. Inequality for coefficients of one trigonometric polynomial..pdf
  226. Inequality for n-th term of sequence..pdf
  227. Inequality for ratio of inradius to circumradius in an obtuse triangle..PNG
  228. Inequality for ratio of inradius to altitude to the hypotenuse..PNG
  229. Inequality for secant..PNG
  230. Inequality for secant..pdf
  231. Inequality for sequence defined recursively..PNG
  232. Inequality for sum of distances from incenter to the vertices of a triangle..pdf
  233. Inequality for sum of distances from incenter to vertices in a triangle..PNG
  234. Inequality for sum of weighted integer parts..PNG
  235. Inequality for three non coplanar vectors..pdf
  236. Inequality for two sequences defined recursively..PNG
  237. Inequality from Crux..PNG
  238. Inequality from Vietnam 1988 MO..PNG
  239. Inequality from West German Math Olympiad, 1982..PNG
  240. Inequality in a right triangle..pdf
  241. Inequality in a triangle involving side lengths, medians and product of cosines..PNG
  242. Inequality in a triangle involving square roots and sine..PNG
  243. Inequality in a triangle with cosine, sine, inradius and semiperimeter..PNG
  244. Inequality in a triangle with side-lengths and semiperimeter..PNG
  245. Inequality in a triangle with squares of medians and side lengths.PNG
  246. Inequality in a triangle with symedians..pdf
  247. Inequality in a triangle with vanished variables, circumradius and sidelengths 2..PNG
  248. Inequality in a triangle with vanished variables, circumradius and sidelengths..PNG
  249. Inequality in a triangle..PNG
  250. Inequality in triangle involving medians.pdf
  251. Inequality involving absolute values..PNG
  252. Inequality involving altitudes and circumradius(1 solutution for 2 problems).pdf
  253. Inequality involving altitudes in a non obtuse triangle..PNG
  254. Inequality involving distances from incener to vertices..pdf
  255. Inequality involving equilateral triangles.pdf
  256. Inequality involving factorial and powers of e with natural exponents..PNG
  257. Inequality involving factorial and powers of e with natural exponents.2.PNG
  258. Inequality involving logarithms..PNG
  259. Inequality involving pedal triangle..PNG
  260. Inequality involving quadratic roots..PNG
  261. Inequality involving square roots and logarithms..PNG
  262. Inequality involving square roots in denominator..PNG
  263. Inequality involving square roots of quadratic forms..PNG
  264. Inequality involving square roots..PNG
  265. Inequality involving tan of half angles, sidelengths and radii..PNG
  266. Inequality involving triangles (with midpoints).pdf
  267. Inequality involving triangles with vanishing variables..pdf
  268. Inequality involving triangles.pdf
  269. Inequality normalized by abc=1.pdf
  270. Inequality of George Apostolopuolos..PNG
  271. Inequality of George Apostolopuolos..pdf
  272. Inequality on hyperplane..PNG
  273. Inequality that equivalent to inequality with delta polynomial..pdf
  274. Inequality which looks easy but in fact it isn't so..PNG
  275. Inequality with 2 variables, sol.2.PNG
  276. Inequality with 2 variables..PNG
  277. Inequality with 4 variable and quadratic roots..PNG
  278. Inequality with AM and GM.PNG
  279. Inequality with Fibonacci numbers.PNG
  280. Inequality with R, r and max. altitude in a non-obtuse triangle..pdf
  281. Inequality with R, r and max. altitude..pdf
  282. Inequality with altitudes, circumradius and inradius in a triangle..pdf
  283. Inequality with angle bisectors and squares of side lengths in a triangle.PNG
  284. Inequality with angle bisectors, extended angle bisectors and sinuses..pdf
  285. Inequality with area of pedal triangle for centroid of an acute angled triangle..PNG
  286. Inequality with areas and distances in a triangle..PNG
  287. Inequality with areas of bisectorial triangles..pdf
  288. Inequality with binomial coefficients..PNG
  289. Inequality with circumradius of Median Triangle..PNG
  290. Inequality with constraint that involve cubic root..pdf
  291. Inequality with cubic roots.PNG
  292. Inequality with cyclic summation.pdf
  293. Inequality with distances from incenter to vertices and circumcircle..PNG
  294. Inequality with distances from interior point of a triangle to its vertices and side lengths..PNG
  295. Inequality with distances from interior point of a triangle to its vertices..PNG
  296. Inequality with distances in an equilateral triangle..PNG
  297. Inequality with e and pi..pdf
  298. Inequality with exponential and trigonometric functions..PNG
  299. Inequality with extended angle bisectors..pdf
  300. Inequality with four components.pdf
  301. Inequality with four variables..pdf
  302. Inequality with fractional and integer parts..PNG
  303. Inequality with generalization..pdf
  304. Inequality with geometric interpretation..pdf
  305. Inequality with harmonic numbers..pdf
  306. Inequality with log..PNG
  307. Inequality with logarithm and product of roots from natural numbers..PNG
  308. Inequality with logarithm.pdf
  309. Inequality with logarithms and exponents..pdf
  310. Inequality with logarithms..PNG
  311. Inequality with logarithms.PNG
  312. Inequality with medians, altitudes and cos.pdf
  313. Inequality with medians, inradius and sines..PNG
  314. Inequality with medians, side lengths and area..PNG
  315. Inequality with medians, side lengths and cosines in an acute triangle..PNG
  316. Inequality with multiplicative nested radicals..pdf
  317. Inequality with n distinct positive integers..PNG
  318. Inequality with n variables and square roots in denominators..PNG
  319. Inequality with n+1 positive real numbers..PNG
  320. Inequality with n-th powers of two binomials..PNG
  321. Inequality with n-variables and constraint in inequality form..PNG
  322. Inequality with one variable & two exponents..pdf
  323. Inequality with polynomial and its derivative..PNG
  324. Inequality with polynomial and x in power x.PNG
  325. Inequality with powers of three binomials 2..PNG
  326. Inequality with powers of three binomials..PNG
  327. Inequality with product of logarithms..PNG
  328. Inequality with product of three shifted squeres.pdf
  329. Inequality with quadratic constraint in R..pdf
  330. Inequality with quadratic normalization..PNG
  331. Inequality with ratio e to pi..PNG
  332. Inequality with ratio of two nested quadratic roots..pdf
  333. Inequality with reciprocal constraint(copy).png
  334. Inequality with refinement.pdf
  335. Inequality with side lengths, altitudes and circumradius..pdf
  336. Inequality with side lengths, cosine and area in a triangle..PNG
  337. Inequality with six variables..PNG
  338. Inequality with square roots.PNG
  339. Inequality with squares of cosines and side lengths. Corrected version of the problem..PNG
  340. Inequality with sum of cubes and product.pdf
  341. Inequality with sum of powers..pdf
  342. Inequality with sum of ratios bisector to median..pdf
  343. Inequality with sum of squares in denumerator..pdf
  344. Inequality with sum of squares of logarithms..PNG
  345. Inequality with the product.PNG
  346. Inequality with three inradii in a right-angled triangle..PNG
  347. Inequality with three real variables subject to constraint..PNG
  348. Inequality with three variables (5359.SSMJ)..PNG
  349. Inequality with three variables involving square roots..PNG
  350. Inequality with two variables and quadratic roots..PNG
  351. Inequality with two variables and unusual constraint..PNG
  352. Inequality with two variables in triangular domain..PNG
  353. Inequality with unusual constraint..PNG
  354. Inequality with vanished variables..PNG
  355. Inequality with vanished variables.pdf
  356. Inequality with variations..PNG
  357. Inequality with x-y,y-z,z-x..PNG
  358. Inequality.pdf
  359. Infinite product for a sequence defined by quadratic recurrence..PNG
  360. Infinite series with harmonic numbers.pdf
  361. Infinite sum in the third degree..pdf
  362. Infinite sum related to number e..PNG
  363. Infinite sum with arccos..PNG
  364. Integer part of n-th term of one sequence..PNG
  365. Integer part of numerical expression which is always odd number.PNG
  366. Integer part of one sum2.pdf
  367. Integer value of expression with radicals.pdf
  368. Integral equation.PNG
  369. Inverse to Erdos-Mordell inequality.pdf
  370. Investigation of some inequality..pdf
  371. Investigation ofsomeinequality(short).PNG
  372. Irrational function which value for any term of one sequence is an integer number..PNG
  373. Irrationality of one numerical expression..PNG
  374. J258.Sol..PNG
  375. J421. Sol..pdf
  376. J423. Sol..pdf
  377. J425. Sol..pdf
  378. J87. Official solutions.pdf
  379. Klamkin Quickies (OC-213).pdf
  380. Lalescu kind limit involving radical superfactorial..PNG
  381. Length of an angle bisector..PNG
  382. Like triangle inequality involving area..PNG
  383. Limit calculation.pdf
  384. Limit involving binomial coefficients..PNG
  385. Limit involving fractional part..PNG
  386. Limit of a n-th root of the sequence which defined by convolutive recurrence relation..PNG
  387. Limit of one more Lalescu kind sequence..pdf
  388. Limit of sequence defined by system of two linear recurrences..PNG
  389. Limit of sequence via integral..PNG
  390. Limit with a composite Sine..pdf
  391. Limit with iterated logarithm.(solution).PNG
  392. Limit with logarithmic and exponential functions..PNG
  393. Limit with product of binomial coefficients..PNG
  394. Limit with ratios of natural logarithms..PNG
  395. Limit with shifted harmonic numbers..pdf
  396. Limit with the product of tangents..PNG
  397. Limit, involving sum of binomial coefficients..PNG
  398. Linear Fractional recurrenceture.PNG
  399. Llimit with binomial coefficients.pdf
  400. Logarithmic Inequalities with AM & GM.pdf
  401. Lower and upper bounds for difference btween 3n-th and n-th harmonic numbers..PNG
  402. Lower and upper bounds.... Remark..PNG
  403. Lower bound for sum of medians in non-obtuse triangle..pdf
  404. Lower bound for sum of ratios of side length to length of angle bisector..PNG
  405. Lower bound for sum of squres of ratios altitudes to sidelengts.pdf
  406. MH67, AMJ-vol.6, n.1,2019.PNG
  407. MR6, 2015 All solutions in one file..pdf
  408. Main geometric Inequality..PNG
  409. Majorant for sum of products side lengths and medians.PNG
  410. Maximization of one function involving absolute values..PNG
  411. Maximization without calculus..PNG
  412. Maximum and minimum values of one trigonometric function..PNG
  413. Maximum of function three variables..PNG
  414. Maximum of product of three paired differences.pdf
  415. Maximum value of an expression..PNG
  416. Maximum value of one cyclic expression.PNG
  417. Min, max problem with constraint for the product of two sum with rational expressions..PNG
  418. Min, max problem with constraint..PNG
  419. Minimal value of one polynomial..PNG
  420. Minimization of one 3-variables function with constraint without Lagrange multiplier principle.pdf
  421. Minimization sum of wieghted distances in a triangle..pdf
  422. Minimum of one trigonometric expression in a triangle..PNG
  423. Minorant and majorant for sum of reciprocal to elements of one sequence defined via nonlinear recurrence..PNG
  424. Minorant for one sum..PNG
  425. Minorant for sum of two sequences defined by system of recurrences..PNG
  426. Modification of Weitzenböck's inequality.PNG
  427. Multidimentional sum with m-th power of min(W15,Octogon, 2017).pdf
  428. Mysterious cubic equation.pdf
  429. Neravenstvo..pdf
  430. Nested cubic roots..pdf
  431. Nested square roots..pdf
  432. No mapping with n fixed n-points..pdf
  433. Non homogeneous inequality..PNG
  434. Nonlinear recurrence which equivalent to linear..pdf
  435. Nonlinear system of equation which equivalent to a linear system..PNG
  436. Not elementary integral..pdf
  437. Number of of ordered triples.PNG
  438. O260. Solution by proposer..pdf
  439. O260_n.3_2013-official solution.pdf
  440. O274. Solution by proposer.PNG
  441. Official solutions to 5435,5436,5437..pdf
  442. One 2-nd digree LH recurrence with nonconstant coefficients (short)..PNG
  443. One 2-nd digree LH recurrence with nonconstant coefficients..PNG
  444. One Genometric Inequality with vanished variables..pdf
  445. One Identity with side-lengths and cosines in a triangle..PNG
  446. One Inequality with angle bisectors..pdf
  447. One Polynomial Mean Inequality.(5417).pdf
  448. One algebraic problem..PNG
  449. One algebraic system with geometric interpretation..PNG
  450. One application of Jensen's Inequality..PNG
  451. One application of Stolz-Cezaro Theorem..PNG
  452. One combinatirix problem.PNG
  453. One conflicting inequality.pdf
  454. One corollary from Weitzenböck's inequality..PNG
  455. One cyclic geometric inequality..pdf
  456. One cyclic inequality with generalization..pdf
  457. One cyclic inequality with medians and altitudes in a triangle..PNG
  458. One cyclic inequality..PNG
  459. One divisibility problem involving Pell's equation..PNG
  460. One divisibility problem..PNG
  461. One divisibility property related to Pell's eqution x²-2y²=1..PNG
  462. One double inequality for a right triangle..pdf
  463. One double inequality in a triangle..PNG
  464. One double sum.PNG
  465. One equivalent of Schure's Inequality..pdf
  466. One equivalent of Walker Inequality..pdf
  467. One hard trigonometric inequality in a triangle.pdf
  468. One identity related to extended bisectors..PNG
  469. One important property related to spectrum of irrational number bigger 1..pdf
  470. One inequality for obtuse-angled triangle..PNG
  471. One inequality for sum of medians for a non-obtuse triangle..PNG
  472. One inequality instead two..pdf
  473. One inequality instead two.PNG
  474. One inequality involving factorial with improvement..PNG
  475. One inequality involving reciprocal to n real numbers.pdf
  476. One inequality with four variables..PNG
  477. One inequality with integer parts which in fact is equality..PNG
  478. One inequality with sidelengths and circumradius..PNG
  479. One inequality with sidelengths and circumradius..pdf
  480. One inequality with sum of logarithms of natural numbers..PNG
  481. One inequality with three variables involving fractions..PNG
  482. One inequality with two variables (4 solutions).PNG
  483. One inequality with two variables (generalization).PNG
  484. One interesting inequality with cubic constraint..PNG
  485. One interesting inequality..pdf
  486. One limit in Lalescu stile.PNG
  487. One limit involving Euler's constant and logarithm.PNG
  488. One limit of Lalescu kind sequence..pdf
  489. One limit related to e..PNG
  490. One limit with product which related to e..pdf
  491. One limit with superfactorial 2..pdf
  492. One limit with superfactorial.PNG
  493. One maxmin problem in generic terms..PNG
  494. One more limit in Lalescu stile.(Solution).PNG
  495. One more limit of Lalescu kind sequence..pdf
  496. One more limit.pdf
  497. One more sequence that converge to e..pdf
  498. One nonhomogeneous inequality..pdf
  499. One not simple inequality.pdf
  500. One numerical inequality..PNG
  501. One olympiad inequality..pdf
  502. One problem about quadratically connected sequences.pdf
  503. One problem involving Pell equation.pdf
  504. One problem with many solutions..pdf
  505. One problem--three solution..PNG
  506. One product of two complex powers with real positive value..PNG
  507. One really sharp inequality..pdf
  508. One refinament of Weitzenböck's inequality.pdf
  509. One refinement of Reciprocal Inequality..PNG
  510. One sensitive inequality..PNG
  511. One sharp inequality which looks simple..PNG
  512. One simple inequality with many not simple applications..PNG
  513. One sum involving tan in the 3-d degree..PNG
  514. One summation problem..PNG
  515. One symmetric rational inequality with constraint..PNG
  516. One system of congruences..PNG
  517. One trigonometric equation with two variables.PNG
  518. Only Cauchy Inequality..PNG
  519. Parametric limit..PNG
  520. Positivity of the polynomial of even degree that looks like e^{x}..PNG
  521. Power series with Fibonacci coefficients..PNG
  522. Problem 1.13(33-Met. Rec.).pdf
  523. Problem 139..PNG
  524. Problem 4.1(Met.Rec. Pr.90).pdf
  525. Problem 5(Almaty team selection for IZHO,2015)..PNG
  526. Problem 6 from 6-th CGMO,2-nd day,2007..PNG
  527. Problem involving Mobius function in C..pdf
  528. Problem involving continued fractions and the year 2020..PNG
  529. Problem involving continued fractions and the year 2020..pdf
  530. Problem on divisibility..PNG
  531. Problem on finding a limit with asymptotically defined sequences..PNG
  532. Problem on infinite summation involving arctan and year 2020.PNG
  533. Problem with determinant 1..pdf
  534. Problem with determinant 2..pdf
  535. Problem1.(32-nd Russian MO 2005-2006).pdf
  536. Proof 4. of (1)..PNG
  537. Proof of (l_a)²=bc-b₁c₁.PNG
  538. Proofs to three corollaries..pdf
  539. Properties of Arithmetic Progression.pdf
  540. Quadratic decomposition.PNG
  541. Quadratic equation with ⌊x⌋..PNG
  542. Quadratically connected sequences.pdf
  543. Range for three variables that subject to constraint..PNG
  544. Ratio of semiperimeter of an acute triangle to semiperimeter its orthotriangle..PNG
  545. Rationality of square root of some rational function..pdf
  546. Reciprocal inequality..PNG
  547. Recovering of an acute triangle by given sidelengths of its orthic triangle-1.PNG
  548. Recurrent system of equation (Variant of the original version).pdf
  549. Recurrent system of equation(improvisation)..pdf
  550. Recurrent system of equation.pdf
  551. Remark to Another cyclic inequality.PNG
  552. Repeated limit of one two dimensional sequence..PNG
  553. Representation of natural n via sum of squares of rationals numbers..PNG
  554. Representation of quadratic trinomial as linear combination of squares of two binomials..PNG
  555. S-Multidimentional sum with m-th power of min.pdf
  556. S181. Sol..pdf
  557. S289. Sol..PNG
  558. Sequence defined by 3-rd degree recurrence and given asymptotic..pdf
  559. Sequence defined by non linear recursion..PNG
  560. Sequence of integer numbers defined by recurrence that involved square root..PNG
  561. Sequence that generate squares of integers..PNG
  562. Sequence with exclusions..PNG
  563. Series of geometric inequalities..pdf
  564. Sharp Inequality.pdf
  565. Sharp geometric inequality..PNG
  566. Solution 2..PNG
  567. Solution of one non linear recurrence.PNG
  568. Solution2..PNG
  569. Solutions to problems S-35,S-36,S-37.pdf
  570. Strange inequality..PNG
  571. Strange inequality.pdf
  572. Sum involving tan and cos..PNG
  573. Sum of 3 quadratic roots inequality.PNG
  574. Sum of distances from circumcenter to the sides..PNG
  575. Sum of integer parts from square roots.PNG
  576. Sum of naturally weighted squares of binomial coefficients ..PNG
  577. Sum of squares of tangents and Chebishev Polynomials..pdf
  578. Sum of the cubes of the first n Fibonacci's numbers..pdf
  579. Sum of three fraction wich is integer for any integer n..PNG
  580. Sum with integer parts of quadratic roots.pdf
  581. Sum with integer parts..PNG
  582. Sum with tangents in square..pdf
  583. Superproblem with some irrational recurrence..PNG
  584. Superproblem with some irrational recurrence..pdf
  585. Superstable triangle.(MOG variant).pdf
  586. Symmetric inequality with asymmetric condition of equality 2..PNG
  587. Symmetric inequality with asymmetric condition of equality..pdf
  588. Symmetric inequality with asymmetric condition of equality..png
  589. Symmetric inequality with three variable and quadratic roots in denominators..PNG
  590. Symmetric inequality with three variables involving fractions..PNG
  591. Symmetric majorant for cyclic expression involving square roots..PNG
  592. System of equations involving determinant..pdf
  593. TOTTEN-11..pdf
  594. The greatest integer value of x(modified).pdf
  595. The least positive integer N..pdf
  596. The small investigation about one problem.pdf
  597. The sum of the series..PNG
  598. The value of the sum can be calculated, for example,by the such way..PNG
  599. Three ODE (Filippov 127-129) for MOG.PNG
  600. Three applications of AM-GM Inequality..pdf
  601. Three inequalities with 2 variables(solutions)..PNG
  602. Three inequalities...pdf
  603. Three perfect squares..PNG
  604. Three problems on sequences defined recursively..pdf
  605. Three proofs of one inequality..PNG
  606. Totally inverse inequality.pdf
  607. Triangle defined by lengths of two sides and lengths of angle bisector..PNG
  608. Triangles with largest integer semiperimeter..pdf
  609. Trig helps algebra-Solve the system..pdf
  610. Trig. equation (5.412. Skanavi).PNG
  611. Trig. equation with solutions in integers.pdf
  612. Trig. inequality with tangents-5454 SSMJ.pdf
  613. Trigonometric identity involving inverse cos and tan..PNG
  614. Trigonometric inequality in acute triangle.pdf
  615. Trigonometric inequality-S110..PNG
  616. Trigonometry helps algebra..PNG
  617. Two convertible inequalities..PNG
  618. Two inequalities for a sequence defined by nonlinear recurrence..PNG
  619. Two inequalities proposed by Mihaly Bencze..PNG
  620. Two inequalities with exradii and altitudes..pdf
  621. Two inequalities.pdf
  622. Two inequality instead one..PNG
  623. Two infinite nested roots..pdf
  624. Two linked sequences..pdf
  625. Two orthogonal segments in a isosceles triangle..pdf
  626. Two problems with Fibonacci numbers..PNG
  627. Two problems with inequalities..PNG
  628. Two proofs of one inequality..PNG
  629. Two quadratically connected sequences..PNG
  630. Two quadratically connected sequences..pdf
  631. Two solutions to one problem..PNG
  632. Two solutions..PNG
  633. Two strictly monotonic and unbounded secuences..pdf
  634. Two sums.pdf
  635. Two way to calculate one limit Sol.2.PNG
  636. Two way to calculate one limit. Sol.1.PNG
  637. U259. Sol. by proposer..pdf
  638. U271.Sol..pdf
  639. Upper bound for area of a triangle via lengths of bisectors.PNG
  640. Upper bound for nested n square roots..PNG
  641. Upper bound for one sum..PNG
  642. Upper bound for product of two medians..pdf
  643. Upper bound for sum of the first n terms of one sequence defined recursively..PNG
  644. Upper bound of one sum which defined via nonlinear recurrence.PNG
  645. Upper bound via lower bound..PNG
  646. Using Lagrange's identity.PNG
  647. Using invariant(edited).PNG
  648. Value of one algebraic expression.PNG
  649. Variant of the problem with softer claim to b..PNG
  650. Vector interpretation of one algebraic inequality..pdf
  651. Very transcendental equation..PNG
  652. W1 2014. Solution..pdf
  653. W10( J.Wildt IMC 2016)-solution.PNG
  654. W10-official solutions (J. Wildt IMO 2016).pdf
  655. W12, 2016-solutions.pdf
  656. W15-official solutions (J. Wildt IMO 2016).pdf
  657. W21,2016_ Solution..pdf
  658. W26,2016_Solutions.pdf
  659. W27,2016_Solutions.pdf
  660. W28,2016_Solutions..pdf
  661. W29, 2016-official solutions with adddition.pdf
  662. W31,2016_Solutions.pdf
  663. W4 2014. Solution.pdf
  664. W6,W7- official solutions (J. Wildt IMO 2016).pdf
  665. W7 2014 Solution 2..pdf
  666. W9 2016- solutions.pdf
  667. Wallis Formula..PNG
  668. Weighted minimization with squares of distances in a triangle..pdf
  669. Without L'Hopital's Rule..PNG
  670. Without words.PNG
  671. m + n + p.pdf
  672. p=a+b+c,q=ab+bc+ca,r=abc.pdf
  673. s,r minorant for product of angle bisectors in a triangle..PNG