Understand the problem Suppose that for a prime number and integers the following holds:Prove that . Source of the problem Baltic Way 2009 Topic Number Theory Difficulty Level Medium Suggested Book Elementary Number Theory by David Burton Start with hints Hint 0Hint...

Understand the problem Given that the number is an integer where and are prime positive numbers, determine . Source of the problem Danube 2014 Topic Number Theory Difficulty Level Easy Suggested Book An Excursion in Mathematics Start with hints Hint 0Hint 1Hint...

Understand the problem Let be the area of the triangle . A non-regular convex polygon is called guayaco if exists a point in its interior such thatShow that, for every integer , a guayaco polygon of sides exists. Source of the problem Cono sur olympiad 2017 Topic...

Understand the problem Prove that the number of ordered triples in the set of residues of such that , where and is prime is . Source of the problem Brazilian Olympiad Revenge 2010 Topic Number Theory Difficulty Level Medium Suggested Book Elementary Number Theory...

Understand the problem Let be the lengths of sides of a (possibly degenerate) triangle. Prove the inequality Let be the lengths of sides of a triangle. Prove the inequality Source of the problem Caucasus Mathematical Olympiad Topic Inequalities Difficulty Level Easy...