Select Page ## Baltic Way 2009

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... ## A fraction involving primes

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... ## A taste of affine transformations

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... ## Solving a congruence

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... ## Inequality involving sides of a triangle

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...