INMO 2020 Problem 4

Let be an integer and be real numbers satisfying . If then prove that . Hint 1Hint 2Hint 3 The conditions hint at inequalities involving an order, such as the rearrangement and Chebychev inequalities. Also note that for all is an equality case, hence we should try to...
The best exponent for an inequality

The best exponent for an inequality

Understand the problem Let  be positive real numbers such that .Find with proof that  is the minimal value for which the following inequality holds: Source of the problem Albania IMO TST 2013 Topic Inequalities Difficulty Level Medium Suggested Book Inequalities by BJ...
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...
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...