A functional inequation

A functional inequation

Understand the problem Find all functions  such thatholds for all . Source of the problem Benelux MO 2013 Topic Functional Equations Difficulty Level Easy Suggested Book Functional Equations by BJ Venkatachala Start with hints Hint 0Hint 1Hint 2Hint 3Hint 4 Do you...
Mathematical Circles Inequality Problem

Mathematical Circles Inequality Problem

Understand the problem If (a,b) are positive reals such that (a+b<2) ,then prove that  $$ displaystyle frac {1}{1+a^2} + frac {1}{1+b^2} leq frac {2}{1+ab} $$ Source of the problem Mathematical Circles Topic Inequality involving AM-GM Difficulty Level Medium...
RMO 2019

RMO 2019

RMO 2019 Regional Mathematics Olympiad, India 2019… welcome to the festival of mathematics  Tool box for Regional Math Olympiad 2019 Geometry Tools for RMO Read More Number Theory Tools for RMO Read More Combinatorics Tools for RMO Read More Algebra Tools for...
AMC 2019 12A Problem 15 Diophantine Equation

AMC 2019 12A Problem 15 Diophantine Equation

Understand the problem Positive real numbers  and  have the property thatand all four terms on the left are positive integers, where log denotes the base 10 logarithm. What is ? Source of the problem 2019 AMC 12A Problems/Problem 15 Topic logarithm, diophantine...
Repunits in arbitrary bases

Repunits in arbitrary bases

Understand the problem find all integers  such us  is a perfect square. Source of the problem New Zealand team training 2004 Topic Number Theory Difficulty Level Medium Suggested Book An Excursion in Mathematics Start with hints Hint 0Hint 1Hint 2Hint 3Hint 4 Do you...