Publications

🖼️ !Inequality with log.PNG

📄 1012. Sol...pdf

📄 1021. Sol..pdf

📄 1022. Sol..pdf

📄 1023. Sol..pdf

📄 1026.Sol..pdf

📄 1036,1037,1038-Solutions..pdf

📄 1037. Sol..pdf

📄 1038. Sol..pdf

📄 1041. Sol..pdf

🖼️ 1076.Sol..PNG

🖼️ 1079.Sol..PNG

🖼️ 1080.Sol..PNG

📄 12038. Sol..pdf

📄 12057(a) Sol..pdf

📄 2580,2581,2585. Sol..pdf

📄 3123, 3125-solutions.pdf

🖼️ 3167. CRUX v.33,n.6. Official solution..PNG

🖼️ 3167. Solution by proposer..PNG

📄 3329.Solution by proposer..pdf

📄 3719. Sol..pdf

📄 3729. Sol..pdf

🖼️ 3941,3942 CRUX vol.40,n.5.PNG

🖼️ 3946. Two inequalities with internal angle bisectors.PNG

🖼️ 3948. Crux v.40,n.5 -Solution.PNG

📄 3961. Sol..pdf

📄 3964. Sol..pdf

📄 3965. Sol..pdf

📄 3970. Sol..pdf

📄 4013. Official solutions..pdf

📄 4103. Sol..pdf

📄 4103.Sol..pdf

📄 4158.Sol..pdf

🖼️ 4207. Proposed by Mihaela Berindeanu..PNG

📄 4306. Solution..pdf

📄 4308.Sol.pdf

📄 4348. Sol..pdf

📄 4491. Sol..pdf

📄 4493. Sol..pdf

📄 5211-official solutions 11.-2012.pdf

📄 5335. Official solutions..pdf

📄 5338. Solution by proposer..pdf

🖼️ 5358. Solution by proposer..PNG

📄 5359. Three official solutions.pdf

📄 5387. Official solutions.pdf

📄 5398. Sol.pdf

📄 5400. Solution by proposer.pdf

📄 5404. Four official solutions..pdf

📄 5453. Official solutions..pdf

📄 5453. Sol..pdf

📄 5466._Three official solutions-SSMA (January 2018).pdf

📄 5467._Four official solutions (SSMA-January 2018).pdf

📄 5477. Official solutions..pdf

📄 5478. Official solutions..pdf

📄 5478. Sol..pdf

📄 5495. Official solutions..pdf

📄 5495. Solution.(And one more limit of Lalescu kind sequence.).pdf

📄 5519. Solution.pdf

📄 5525-official solutions..pdf

📄 866. Sol..pdf

📄 936. Solution...pdf

🖼️ A Class of Inequalities_n.1.PNG

🖼️ A Class of Inequalities_n.2(short solution).PNG

🖼️ A Class of Inequalities_n.2.PNG

🖼️ A Class of Inequalities_n.3(J258).Sol..PNG

🖼️ A Class of Inequalities_n.4(S289). Sol..PNG

📄 A point P in the plane of a triangle.pdf

📄 A point P on the circumcircle of a right-angled triangle.pdf

📄 A trigonometric inequality.pdf

🖼️ About natural numbers which is a sum of at least two consecutive naturals..PNG

🖼️ About one inequality with exp. function.PNG

📄 About one inequality. Its proofs and short history.pdf

📄 About one non linear recurrence of the third order.pdf

📄 About polynomials of degree 3.pdf

📄 About two properties of Fibonacci Numbers.pdf

📄 Additions to one problem (calculations of two integrals).pdf

🖼️ After translation..PNG

🖼️ Algebraic equivalent of one geometric inequality in acute triangle..PNG

🖼️ Algebraic equivalent of Walker's Inequality..PNG

🖼️ Algebraic inequality with geometric interpretation 2..PNG

🖼️ Algebraic inequality with geometric interpretation..PNG

🖼️ Algebraic inequality with geometric interpretation3.PNG

📄 Algebraic inequality with trigometric variations..pdf

📄 Algebraic version of triangle inequality for side lengths of Median Triangle..pdf

🖼️ Almost asymptotic inequality.PNG

🖼️ Almost Vieta's system of equations..PNG

📄 Alternating infinite sum with double factorial..pdf

📄 AM-GM inequality with logarithms.pdf

📄 An inequality from IMO 2009 Shortlist from Estonia.pdf

📄 An inequality with radicals..pdf

📄 And again problem related to quadratically connected sequences..pdf

🖼️ And more pair of sequences that quadratically connected..PNG

📄 And one more limit related to e.pdf

🖼️ And without L'Hopital's Rule..PNG

📄 Angel's preserving linear mapping..pdf

🖼️ Another Cyclic inequality(corrected) ..PNG

🖼️ Another proof of inequality (1)..PNG

📄 Anti Reciprocal inequality..pdf

📄 Area of trapezoid(via partial areas).pdf

📄 Area via given partial areas..pdf

📄 Arithmetic progression defined by inequality.pdf

📄 Around main trigonometric identity in a triangle..pdf

🖼️ Asymmetric and nonhomogeneous inequality with three variables with square root..PNG

🖼️ Asymptotic behavior of one sequence defined recursively..PNG

🖼️ Asymptotic behavior of one sequence defined recursively..PNG

📄 Asymptotic of one sum..pdf

🖼️ Asymptotic representation of a sequence defined by non linear recurrence..PNG

🖼️ Asymptotic variant of the problem..PNG

📄 Basic inequalities with distances..pdf

📄 Basic inequality with distances..pdf

📄 Blundon's Inequality.pdf

📄 Calculate limit with product of n differences..pdf

📄 Calculate the limit 2.pdf

📄 Calculate the limit 3.pdf

📄 Calculate the limit 4.pdf

📄 Calculate the limit 5.pdf

📄 Calculate the limit 6.pdf

📄 Calculate the limit 7.pdf

📄 Calculate the limit 8..pdf

📄 Calculate the limit 9..pdf

📄 Calculate the limit with binomomial coefficients.pdf

📄 Calculate the limit with hidden factorial.pdf

📄 Calculate the limit with power-exponential function..pdf

📄 Calculate the limit.pdf

🖼️ Calculate the limit.PNG

📄 Calculate the missing angle.pdf

🖼️ Calculation of one composite series..PNG

📄 Calculation of one infinite sum..pdf

🖼️ Calculation of one limit (without L'Hôpital's rule)..PNG

🖼️ Calculation of one limit by passing to limit under integral..PNG

🖼️ Calculation of the one limit with n-th root and ln.PNG

🖼️ Combined progression..PNG

📄 Compare the numbers(product of logarithms).pdf

🖼️ Compare two product with logarithms..PNG

🖼️ Compute the missing area..PNG

🖼️ Corrected statement of one problem.PNG

🖼️ Corrected statement of one problem_variant 1.PNG

🖼️ Corrected statement of one problem_variant 2.PNG

📄 Corrected variant of the problem..pdf

🖼️ Corrected version.PNG

🖼️ Correction to one limit problem..PNG

🖼️ Correlations between angles of two triangles with sides related by equations..PNG

📄 Counterexamples & correction.pdf

🖼️ Counterexamples & correction.PNG

📄 Criterion for existence of n-periodic orbits of one Mobius function.pdf

🖼️ CRUX 1701-Solution.PNG

🖼️ Cyclic criterion for equilateral triangle..PNG

🖼️ Cyclic form of Schure's inequality(Solution with Wendy's Subst.).PNG

🖼️ Cyclic form of Schure's inequality..PNG

🖼️ Cyclic inequality from Indian TST to the IMO 2002.PNG

🖼️ Cyclic inequality in a triangle..PNG

🖼️ Cyclic inequality involving cube roots..PNG

📄 Cyclic inequality involving square roots.pdf

🖼️ Cyclic inequality with constraint..PNG

🖼️ Cyclic inequality with quadratic roots(variant2)..PNG

📄 Cyclic inequality with quadratic roots..pdf

🖼️ Cyclic inequality with three variable that belong to closed interval..PNG

📄 Cyclic inequality with three variables involving fractions..pdf

🖼️ Cyclic inequality.PNG

📄 Cyclic refinement of reciprocal inequality.pdf

📄 Decomposition of any natural number as sum of squares of rational numbers..pdf

🖼️ Definite integral involving sine, cosine and logarithm..PNG

🖼️ Definite integral with sine and cosine..PNG

📄 Difference representation of one binomial expansion.pdf

🖼️ Difference=perfect square..PNG

🖼️ Differential equation..PNG

🖼️ Divisibility by 40 of a natural numbers that satisfy two quadratic properties..PNG

🖼️ Divisibility property of a one sequence defined recursively.PNG

🖼️ Divisibility property of one sequence defined by nonlinear recurrence..PNG

📄 Double algebraic inequality with geometric interpretation of its right hand side..pdf

🖼️ Double inequality for ratio of double factorials..PNG

📄 Double inequality for variables that belong to a segment..pdf

🖼️ Double inequality for variables that belong to a segment..PNG

📄 Double inequality in N..pdf

📄 Double inequality related to Hyperfactorial.pdf

🖼️ Double inequality with constraint x+y+z=1..PNG

🖼️ Double inequality with GM and AM and involving ln..PNG

🖼️ Double inequality with side lengths, medians, inradius and circumradius..PNG

🖼️ Double inequality with sum of quadratic roots of consecutive natural numbers..PNG

🖼️ Double inequality with three variables and rational constraint..PNG

🖼️ Easy Inequality with n variables that on first glance looks scary..PNG

🖼️ Equation involving product of integer and fractional parts..PNG

📄 Equation with Fibonacci coefficients..pdf

🖼️ Equation with nested roots.png

📄 Evaluate infinite sum with tan..pdf

🖼️ Evaluation of one infinitely nested square roots..PNG

🖼️ Evalution of one limit..PNG

🖼️ Exact Trigonometric Product Mystery.PNG

🖼️ Existence of rational root between 1 and 2..PNG

🖼️ Exotic limit with e.PNG

🖼️ Explicit formula for sequence defined by nonlinear recurrence..PNG

🖼️ Find radius of the circle..PNG

🖼️ Find the minimum value....PNG

🖼️ Find the value of one cyclic expression.PNG

📄 FQ_H840.pdf

🖼️ Functional equation in continuous functions. (2).PNG

📄 Functional equation in polynomial functions..pdf

📄 Functional equation on N..pdf

📄 Functional equation with twice iterated function.pdf

🖼️ Functional equation.(U182).PNG

🖼️ Functional equation..PNG

🖼️ Generalization of 220. (Vu Duc Canh).PNG

🖼️ Generalization of Cyclic inequality from Indian TST to the IMO 2002.PNG

📄 Generalization of inequality involving sum with abs of differences..pdf

🖼️ Generalization of one limit..PNG

📄 Generation of all rational numbers in (0,1)..pdf

📄 Geometric inequalities involving a,b,c,r,R.pdf

📄 Geometric Inequalities with polynomial 2xy+2yz+2zx2-sqr(x)-sqr(y)-sqr(z), v.22,n.2- 2014.pdf

📄 Geometric inequality with maximal altitude..pdf

🖼️ Hard inequality.PNG

📄 Hard.pdf

🖼️ Hyperbola and Orthocenter Mystery..PNG

📄 Identity involving binomial coefficients with additions..pdf

🖼️ Identity with distances in equilateral triangle..PNG

🖼️ Identity with integer parts involving three square roots..PNG

🖼️ Identity with integer parts..PNG

📄 Identity with product of sines..pdf

📄 Identity with sum of binomial coefficients.pdf

🖼️ Identity with sum that involve binomial coefficients..PNG

📄 Identity(Two sums with integer parts)..pdf

🖼️ Inequalities with powers of binomials 1+x,1-x.PNG

📄 Inequalities with two variables Cut the Knot.pdf

🖼️ Inequality for a sequence defined by recurrence.PNG

🖼️ Inequality for acute tringle with tan and sec..PNG

📄 Inequality for coefficients of one trigonometric polynomial..pdf

📄 Inequality for n-th term of sequence..pdf

🖼️ Inequality for ratio of inradius to circumradius in an obtuse triangle..PNG

🖼️ Inequality for ratio of inradius to altitude to the hypotenuse..PNG

📄 Inequality for secant..pdf

🖼️ Inequality for secant..PNG

🖼️ Inequality for sequence defined recursively..PNG

📄 Inequality for sum of distances from incenter to the vertices of a triangle..pdf

🖼️ Inequality for sum of distances from incenter to vertices in a triangle..PNG

🖼️ Inequality for sum of weighted integer parts..PNG

📄 Inequality for three non coplanar vectors..pdf

🖼️ Inequality for two sequences defined recursively..PNG

🖼️ Inequality from Crux..PNG

🖼️ Inequality from Vietnam 1988 MO..PNG

🖼️ Inequality from West German Math Olympiad, 1982..PNG

📄 Inequality in a right triangle..pdf

🖼️ Inequality in a triangle involving side lengths, medians and product of cosines..PNG

🖼️ Inequality in a triangle involving square roots and sine..PNG

🖼️ Inequality in a triangle with cosine, sine, inradius and semiperimeter..PNG

🖼️ Inequality in a triangle with side-lengths and semiperimeter..PNG

🖼️ Inequality in a triangle with squares of medians and side lengths.PNG

📄 Inequality in a triangle with symedians..pdf

🖼️ Inequality in a triangle with vanished variables, circumradius and sidelengths 2..PNG

🖼️ Inequality in a triangle with vanished variables, circumradius and sidelengths..PNG

🖼️ Inequality in a triangle..PNG

📄 Inequality in triangle involving medians.pdf

🖼️ Inequality involving absolute values..PNG

📄 Inequality involving altitudes and circumradius(1 solutution for 2 problems).pdf

🖼️ Inequality involving altitudes in a non obtuse triangle..PNG

📄 Inequality involving distances from incener to vertices..pdf

📄 Inequality involving equilateral triangles.pdf

🖼️ Inequality involving factorial and powers of e with natural exponents..PNG

🖼️ Inequality involving factorial and powers of e with natural exponents.2.PNG

🖼️ Inequality involving logarithms..PNG

🖼️ Inequality involving pedal triangle..PNG

🖼️ Inequality involving quadratic roots..PNG

🖼️ Inequality involving square roots and logarithms..PNG

🖼️ Inequality involving square roots in denominator..PNG

🖼️ Inequality involving square roots of quadratic forms..PNG

🖼️ Inequality involving square roots..PNG

🖼️ Inequality involving tan of half angles, sidelengths and radii..PNG

📄 Inequality involving triangles (with midpoints).pdf

📄 Inequality involving triangles with vanishing variables..pdf

📄 Inequality involving triangles.pdf

📄 Inequality normalized by abc=1.pdf

📄 Inequality of George Apostolopuolos..pdf

🖼️ Inequality of George Apostolopuolos..PNG

🖼️ Inequality on hyperplane..PNG

📄 Inequality that equivalent to inequality with delta polynomial..pdf

🖼️ Inequality which looks easy but in fact it isn't so..PNG

🖼️ Inequality with 2 variables, sol.2.PNG

🖼️ Inequality with 2 variables..PNG

🖼️ Inequality with 4 variable and quadratic roots..PNG

📄 Inequality with altitudes, circumradius and inradius in a triangle..pdf

🖼️ Inequality with AM and GM.PNG

🖼️ Inequality with angle bisectors and squares of side lengths in a triangle.PNG

📄 Inequality with angle bisectors, extended angle bisectors and sinuses..pdf

🖼️ Inequality with area of pedal triangle for centroid of an acute angled triangle..PNG

🖼️ Inequality with areas and distances in a triangle..PNG

📄 Inequality with areas of bisectorial triangles..pdf

🖼️ Inequality with binomial coefficients..PNG

🖼️ Inequality with circumradius of Median Triangle..PNG

📄 Inequality with constraint that involve cubic root..pdf

🖼️ Inequality with cubic roots.PNG

📄 Inequality with cyclic summation.pdf

🖼️ Inequality with distances from incenter to vertices and circumcircle..PNG

🖼️ Inequality with distances from interior point of a triangle to its vertices and side lengths..PNG

🖼️ Inequality with distances from interior point of a triangle to its vertices..PNG

🖼️ Inequality with distances in an equilateral triangle..PNG

📄 Inequality with e and pi..pdf

🖼️ Inequality with exponential and trigonometric functions..PNG

📄 Inequality with extended angle bisectors..pdf

🖼️ Inequality with Fibonacci numbers.PNG

📄 Inequality with four components.pdf

📄 Inequality with four variables..pdf

🖼️ Inequality with fractional and integer parts..PNG

📄 Inequality with generalization..pdf

📄 Inequality with geometric interpretation..pdf

📄 Inequality with harmonic numbers..pdf

🖼️ Inequality with log..PNG

🖼️ Inequality with logarithm and product of roots from natural numbers..PNG

📄 Inequality with logarithm.pdf

📄 Inequality with logarithms and exponents..pdf

🖼️ Inequality with logarithms..PNG

🖼️ Inequality with logarithms.PNG

📄 Inequality with medians, altitudes and cos.pdf

🖼️ Inequality with medians, inradius and sines..PNG

🖼️ Inequality with medians, side lengths and area..PNG

🖼️ Inequality with medians, side lengths and cosines in an acute triangle..PNG

📄 Inequality with multiplicative nested radicals..pdf

🖼️ Inequality with n distinct positive integers..PNG

🖼️ Inequality with n variables and square roots in denominators..PNG

🖼️ Inequality with n+1 positive real numbers..PNG

🖼️ Inequality with n-th powers of two binomials..PNG

🖼️ Inequality with n-variables and constraint in inequality form..PNG

📄 Inequality with one variable & two exponents..pdf

🖼️ Inequality with polynomial and its derivative..PNG

🖼️ Inequality with polynomial and x in power x.PNG

🖼️ Inequality with powers of three binomials 2..PNG

🖼️ Inequality with powers of three binomials..PNG

🖼️ Inequality with product of logarithms..PNG

📄 Inequality with product of three shifted squeres.pdf

📄 Inequality with quadratic constraint in R..pdf

🖼️ Inequality with quadratic normalization..PNG

📄 Inequality with R, r and max. altitude in a non-obtuse triangle..pdf

📄 Inequality with R, r and max. altitude..pdf

🖼️ Inequality with ratio e to pi..PNG

📄 Inequality with ratio of two nested quadratic roots..pdf

🖼️ Inequality with reciprocal constraint(copy).png

📄 Inequality with refinement.pdf

📄 Inequality with side lengths, altitudes and circumradius..pdf

🖼️ Inequality with side lengths, cosine and area in a triangle..PNG

🖼️ Inequality with six variables..PNG

🖼️ Inequality with square roots.PNG

🖼️ Inequality with squares of cosines and side lengths. Corrected version of the problem..PNG

📄 Inequality with sum of cubes and product.pdf

📄 Inequality with sum of powers..pdf

📄 Inequality with sum of ratios bisector to median..pdf

📄 Inequality with sum of squares in denumerator..pdf

🖼️ Inequality with sum of squares of logarithms..PNG

🖼️ Inequality with the product.PNG

🖼️ Inequality with three inradii in a right-angled triangle..PNG

🖼️ Inequality with three real variables subject to constraint..PNG

🖼️ Inequality with three variables (5359.SSMJ)..PNG

🖼️ Inequality with three variables involving square roots..PNG

🖼️ Inequality with two variables and quadratic roots..PNG

🖼️ Inequality with two variables and unusual constraint..PNG

🖼️ Inequality with two variables in triangular domain..PNG

🖼️ Inequality with unusual constraint..PNG

🖼️ Inequality with vanished variables..PNG

📄 Inequality with vanished variables.pdf

🖼️ Inequality with variations..PNG

🖼️ Inequality with x-y,y-z,z-x..PNG

📄 Inequality.pdf

🖼️ Infinite product for a sequence defined by quadratic recurrence..PNG

📄 Infinite series with harmonic numbers.pdf

📄 Infinite sum in the third degree..pdf

🖼️ Infinite sum related to number e..PNG

🖼️ Infinite sum with arccos..PNG

🖼️ Integer part of n-th term of one sequence..PNG

🖼️ Integer part of numerical expression which is always odd number.PNG

📄 Integer part of one sum2.pdf

📄 Integer value of expression with radicals.pdf

🖼️ Integral equation.PNG

📄 Inverse to Erdos-Mordell inequality.pdf

📄 Investigation of some inequality..pdf

🖼️ Investigation ofsomeinequality(short).PNG

🖼️ Irrational function which value for any term of one sequence is an integer number..PNG

🖼️ Irrationality of one numerical expression..PNG

🖼️ J258.Sol..PNG

📄 J421. Sol..pdf

📄 J423. Sol..pdf

📄 J425. Sol..pdf

📄 J87. Official solutions.pdf

📄 Klamkin Quickies (OC-213).pdf

🖼️ Lalescu kind limit involving radical superfactorial..PNG

🖼️ Length of an angle bisector..PNG

🖼️ Like triangle inequality involving area..PNG

📄 Limit calculation.pdf

🖼️ Limit involving binomial coefficients..PNG

🖼️ Limit involving fractional part..PNG

🖼️ Limit of a n-th root of the sequence which defined by convolutive recurrence relation..PNG

📄 Limit of one more Lalescu kind sequence..pdf

🖼️ Limit of sequence defined by system of two linear recurrences..PNG

🖼️ Limit of sequence via integral..PNG

📄 Limit with a composite Sine..pdf

🖼️ Limit with iterated logarithm.(solution).PNG

🖼️ Limit with logarithmic and exponential functions..PNG

🖼️ Limit with product of binomial coefficients..PNG

🖼️ Limit with ratios of natural logarithms..PNG

📄 Limit with shifted harmonic numbers..pdf

🖼️ Limit with the product of tangents..PNG

🖼️ Limit, involving sum of binomial coefficients..PNG

🖼️ Linear Fractional recurrenceture.PNG

📄 Llimit with binomial coefficients.pdf

📄 Logarithmic Inequalities with AM & GM.pdf

🖼️ Lower and upper bounds for difference btween 3n-th and n-th harmonic numbers..PNG

🖼️ Lower and upper bounds.... Remark..PNG

📄 Lower bound for sum of medians in non-obtuse triangle..pdf

🖼️ Lower bound for sum of ratios of side length to length of angle bisector..PNG

📄 Lower bound for sum of squres of ratios altitudes to sidelengts.pdf

📄 m + n + p.pdf

🖼️ Main geometric Inequality..PNG

🖼️ Majorant for sum of products side lengths and medians.PNG

🖼️ Maximization of one function involving absolute values..PNG

🖼️ Maximization without calculus..PNG

🖼️ Maximum and minimum values of one trigonometric function..PNG

🖼️ Maximum of function three variables..PNG

📄 Maximum of product of three paired differences.pdf

🖼️ Maximum value of an expression..PNG

🖼️ Maximum value of one cyclic expression.PNG

🖼️ MH67, AMJ-vol.6, n.1,2019.PNG

🖼️ Min, max problem with constraint for the product of two sum with rational expressions..PNG

🖼️ Min, max problem with constraint..PNG

🖼️ Minimal value of one polynomial..PNG

📄 Minimization of one 3-variables function with constraint without Lagrange multiplier principle.pdf

📄 Minimization sum of wieghted distances in a triangle..pdf

🖼️ Minimum of one trigonometric expression in a triangle..PNG

🖼️ Minorant and majorant for sum of reciprocal to elements of one sequence defined via nonlinear recurrence..PNG

🖼️ Minorant for one sum..PNG

🖼️ Minorant for sum of two sequences defined by system of recurrences..PNG

🖼️ Modification of Weitzenböck's inequality.PNG

📄 MR6, 2015 All solutions in one file..pdf

📄 Multidimentional sum with m-th power of min(W15,Octogon, 2017).pdf

📄 Mysterious cubic equation.pdf

📄 Neravenstvo..pdf

📄 Nested cubic roots..pdf

📄 Nested square roots..pdf

📄 No mapping with n fixed n-points..pdf

🖼️ Non homogeneous inequality..PNG

📄 Nonlinear recurrence which equivalent to linear..pdf

🖼️ Nonlinear system of equation which equivalent to a linear system..PNG

📄 Not elementary integral..pdf

🖼️ Number of of ordered triples.PNG

📄 O260. Solution by proposer..pdf

📄 O260_n.3_2013-official solution.pdf

🖼️ O274. Solution by proposer.PNG

📄 Official solutions to 5435,5436,5437..pdf

🖼️ One 2-nd digree LH recurrence with nonconstant coefficients (short)..PNG

🖼️ One 2-nd digree LH recurrence with nonconstant coefficients..PNG

🖼️ One algebraic problem..PNG

🖼️ One algebraic system with geometric interpretation..PNG

🖼️ One application of Jensen's Inequality..PNG

🖼️ One application of Stolz-Cezaro Theorem..PNG

🖼️ One combinatirix problem.PNG

📄 One conflicting inequality.pdf

🖼️ One corollary from Weitzenböck's inequality..PNG

📄 One cyclic geometric inequality..pdf

📄 One cyclic inequality with generalization..pdf

🖼️ One cyclic inequality with medians and altitudes in a triangle..PNG

🖼️ One cyclic inequality..PNG

🖼️ One divisibility problem involving Pell's equation..PNG

🖼️ One divisibility problem..PNG

🖼️ One divisibility property related to Pell's eqution x²-2y²=1..PNG

📄 One double inequality for a right triangle..pdf

🖼️ One double inequality in a triangle..PNG

🖼️ One double sum.PNG

📄 One equivalent of Schure's Inequality..pdf

📄 One equivalent of Walker Inequality..pdf

📄 One Genometric Inequality with vanished variables..pdf

📄 One hard trigonometric inequality in a triangle.pdf

🖼️ One identity related to extended bisectors..PNG

🖼️ One Identity with side-lengths and cosines in a triangle..PNG

📄 One important property related to spectrum of irrational number bigger 1..pdf

🖼️ One inequality for obtuse-angled triangle..PNG

🖼️ One inequality for sum of medians for a non-obtuse triangle..PNG

📄 One inequality instead two..pdf

🖼️ One inequality instead two.PNG

🖼️ One inequality involving factorial with improvement..PNG

📄 One inequality involving reciprocal to n real numbers.pdf

📄 One Inequality with angle bisectors..pdf

🖼️ One inequality with four variables..PNG

🖼️ One inequality with integer parts which in fact is equality..PNG

📄 One inequality with sidelengths and circumradius..pdf

🖼️ One inequality with sidelengths and circumradius..PNG

🖼️ One inequality with sum of logarithms of natural numbers..PNG

🖼️ One inequality with three variables involving fractions..PNG

🖼️ One inequality with two variables (4 solutions).PNG

🖼️ One inequality with two variables (generalization).PNG

🖼️ One interesting inequality with cubic constraint..PNG

📄 One interesting inequality..pdf

🖼️ One limit in Lalescu stile.PNG

🖼️ One limit involving Euler's constant and logarithm.PNG

📄 One limit of Lalescu kind sequence..pdf

🖼️ One limit related to e..PNG

📄 One limit with product which related to e..pdf

📄 One limit with superfactorial 2..pdf

🖼️ One limit with superfactorial.PNG

🖼️ One maxmin problem in generic terms..PNG

🖼️ One more limit in Lalescu stile.(Solution).PNG

📄 One more limit of Lalescu kind sequence..pdf

📄 One more limit.pdf

📄 One more sequence that converge to e..pdf

📄 One nonhomogeneous inequality..pdf

📄 One not simple inequality.pdf

🖼️ One numerical inequality..PNG

📄 One olympiad inequality..pdf

📄 One Polynomial Mean Inequality.(5417).pdf

📄 One problem about quadratically connected sequences.pdf

📄 One problem involving Pell equation.pdf

📄 One problem with many solutions..pdf

🖼️ One problem--three solution..PNG

🖼️ One product of two complex powers with real positive value..PNG

📄 One really sharp inequality..pdf

📄 One refinament of Weitzenböck's inequality.pdf

🖼️ One refinement of Reciprocal Inequality..PNG

🖼️ One sensitive inequality..PNG

🖼️ One sharp inequality which looks simple..PNG

🖼️ One simple inequality with many not simple applications..PNG

🖼️ One sum involving tan in the 3-d degree..PNG

🖼️ One summation problem..PNG

🖼️ One symmetric rational inequality with constraint..PNG

🖼️ One system of congruences..PNG

🖼️ One trigonometric equation with two variables.PNG

🖼️ Only Cauchy Inequality..PNG

📄 p=a+b+c,q=ab+bc+ca,r=abc.pdf

🖼️ Parametric limit..PNG

🖼️ Positivity of the polynomial of even degree that looks like e^{x}..PNG

🖼️ Power series with Fibonacci coefficients..PNG

📄 Problem 1.13(33-Met. Rec.).pdf

🖼️ Problem 139..PNG

📄 Problem 4.1(Met.Rec. Pr.90).pdf

🖼️ Problem 5(Almaty team selection for IZHO,2015)..PNG

🖼️ Problem 6 from 6-th CGMO,2-nd day,2007..PNG

📄 Problem involving continued fractions and the year 2020..pdf

🖼️ Problem involving continued fractions and the year 2020..PNG

📄 Problem involving Mobius function in C..pdf

🖼️ Problem on divisibility..PNG

🖼️ Problem on finding a limit with asymptotically defined sequences..PNG

🖼️ Problem on infinite summation involving arctan and year 2020.PNG

📄 Problem with determinant 1..pdf

📄 Problem with determinant 2..pdf

📄 Problem1.(32-nd Russian MO 2005-2006).pdf

🖼️ Proof 4. of (1)..PNG

🖼️ Proof of (l_a)²=bc-b₁c₁.PNG

📄 Proofs to three corollaries..pdf

📄 Properties of Arithmetic Progression.pdf

🖼️ Quadratic decomposition.PNG

🖼️ Quadratic equation with ⌊x⌋..PNG

📄 Quadratically connected sequences.pdf

🖼️ Range for three variables that subject to constraint..PNG

🖼️ Ratio of semiperimeter of an acute triangle to semiperimeter its orthotriangle..PNG

📄 Rationality of square root of some rational function..pdf

🖼️ Reciprocal inequality..PNG

🖼️ Recovering of an acute triangle by given sidelengths of its orthic triangle-1.PNG

📄 Recurrent system of equation (Variant of the original version).pdf

📄 Recurrent system of equation(improvisation)..pdf

📄 Recurrent system of equation.pdf

🖼️ Remark to Another cyclic inequality.PNG

🖼️ Repeated limit of one two dimensional sequence..PNG

🖼️ Representation of natural n via sum of squares of rationals numbers..PNG

🖼️ Representation of quadratic trinomial as linear combination of squares of two binomials..PNG

🖼️ s,r minorant for product of angle bisectors in a triangle..PNG

📄 S-Multidimentional sum with m-th power of min.pdf

📄 S181. Sol..pdf

🖼️ S289. Sol..PNG

📄 Sequence defined by 3-rd degree recurrence and given asymptotic..pdf

🖼️ Sequence defined by non linear recursion..PNG

🖼️ Sequence of integer numbers defined by recurrence that involved square root..PNG

🖼️ Sequence that generate squares of integers..PNG

🖼️ Sequence with exclusions..PNG

📄 Series of geometric inequalities..pdf

🖼️ Sharp geometric inequality..PNG

📄 Sharp Inequality.pdf

🖼️ Solution 2..PNG

🖼️ Solution of one non linear recurrence.PNG

🖼️ Solution2..PNG

📄 Solutions to problems S-35,S-36,S-37.pdf

🖼️ Strange inequality..PNG

📄 Strange inequality.pdf

🖼️ Sum involving tan and cos..PNG

🖼️ Sum of 3 quadratic roots inequality.PNG

🖼️ Sum of distances from circumcenter to the sides..PNG

🖼️ Sum of integer parts from square roots.PNG

🖼️ Sum of naturally weighted squares of binomial coefficients ..PNG

📄 Sum of squares of tangents and Chebishev Polynomials..pdf

📄 Sum of the cubes of the first n Fibonacci's numbers..pdf

🖼️ Sum of three fraction wich is integer for any integer n..PNG

📄 Sum with integer parts of quadratic roots.pdf

🖼️ Sum with integer parts..PNG

📄 Sum with tangents in square..pdf

📄 Superproblem with some irrational recurrence..pdf

🖼️ Superproblem with some irrational recurrence..PNG

📄 Superstable triangle.(MOG variant).pdf

🖼️ Symmetric inequality with asymmetric condition of equality 2..PNG

📄 Symmetric inequality with asymmetric condition of equality..pdf

🖼️ Symmetric inequality with asymmetric condition of equality..png

🖼️ Symmetric inequality with three variable and quadratic roots in denominators..PNG

🖼️ Symmetric inequality with three variables involving fractions..PNG

🖼️ Symmetric majorant for cyclic expression involving square roots..PNG

📄 System of equations involving determinant..pdf

📄 The greatest integer value of x(modified).pdf

📄 The least positive integer N..pdf

📄 The small investigation about one problem.pdf

🖼️ The sum of the series..PNG

🖼️ The value of the sum can be calculated, for example,by the such way..PNG

📄 Three applications of AM-GM Inequality..pdf

🖼️ Three inequalities with 2 variables(solutions)..PNG

📄 Three inequalities...pdf

🖼️ Three ODE (Filippov 127-129) for MOG.PNG

🖼️ Three perfect squares..PNG

📄 Three problems on sequences defined recursively..pdf

🖼️ Three proofs of one inequality..PNG

📄 Totally inverse inequality.pdf

📄 TOTTEN-11..pdf

🖼️ Triangle defined by lengths of two sides and lengths of angle bisector..PNG

📄 Triangles with largest integer semiperimeter..pdf

📄 Trig helps algebra-Solve the system..pdf

🖼️ Trig. equation (5.412. Skanavi).PNG

📄 Trig. equation with solutions in integers.pdf

📄 Trig. inequality with tangents-5454 SSMJ.pdf

🖼️ Trigonometric identity involving inverse cos and tan..PNG

📄 Trigonometric inequality in acute triangle.pdf

🖼️ Trigonometric inequality-S110..PNG

🖼️ Trigonometry helps algebra..PNG

🖼️ Two convertible inequalities..PNG

🖼️ Two inequalities for a sequence defined by nonlinear recurrence..PNG

🖼️ Two inequalities proposed by Mihaly Bencze..PNG

📄 Two inequalities with exradii and altitudes..pdf

📄 Two inequalities.pdf

🖼️ Two inequality instead one..PNG

📄 Two infinite nested roots..pdf

📄 Two linked sequences..pdf

📄 Two orthogonal segments in a isosceles triangle..pdf

🖼️ Two problems with Fibonacci numbers..PNG

🖼️ Two problems with inequalities..PNG

🖼️ Two proofs of one inequality..PNG

📄 Two quadratically connected sequences..pdf

🖼️ Two quadratically connected sequences..PNG

🖼️ Two solutions to one problem..PNG

🖼️ Two solutions..PNG

📄 Two strictly monotonic and unbounded secuences..pdf

📄 Two sums.pdf

🖼️ Two way to calculate one limit Sol.2.PNG

🖼️ Two way to calculate one limit. Sol.1.PNG

📄 U259. Sol. by proposer..pdf

📄 U271.Sol..pdf

🖼️ Upper bound for area of a triangle via lengths of bisectors.PNG

🖼️ Upper bound for nested n square roots..PNG

🖼️ Upper bound for one sum..PNG

📄 Upper bound for product of two medians..pdf

🖼️ Upper bound for sum of the first n terms of one sequence defined recursively..PNG

🖼️ Upper bound of one sum which defined via nonlinear recurrence.PNG

🖼️ Upper bound via lower bound..PNG

🖼️ Using invariant(edited).PNG

🖼️ Using Lagrange's identity.PNG

🖼️ Value of one algebraic expression.PNG

🖼️ Variant of the problem with softer claim to b..PNG

📄 Vector interpretation of one algebraic inequality..pdf

🖼️ Very transcendental equation..PNG

📄 W1 2014. Solution..pdf

🖼️ W10( J.Wildt IMC 2016)-solution.PNG

📄 W10-official solutions (J. Wildt IMO 2016).pdf

📄 W12, 2016-solutions.pdf

📄 W15-official solutions (J. Wildt IMO 2016).pdf

📄 W21,2016_ Solution..pdf

📄 W26,2016_Solutions.pdf

📄 W27,2016_Solutions.pdf

📄 W28,2016_Solutions..pdf

📄 W29, 2016-official solutions with adddition.pdf

📄 W31,2016_Solutions.pdf

📄 W4 2014. Solution.pdf

📄 W6,W7- official solutions (J. Wildt IMO 2016).pdf

📄 W7 2014 Solution 2..pdf

📄 W9 2016- solutions.pdf

🖼️ Wallis Formula..PNG

📄 Weighted minimization with squares of distances in a triangle..pdf

🖼️ Without L'Hopital's Rule..PNG

🖼️ Without words.PNG