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...

Understand the problem Given a circle , let be a point in its interior, and let be a line passing through . Construct with proof using a ruler and compass, all circles which pass through , are tangent to , and whose centres lie on . Source of the problem RMO 2019...

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...

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...

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...