This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

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Found problems: 2

2014 IFYM, Sozopol, 8
Tags: combinatorics , pairs
In a class with $n$ students in the span of $k$ days, each day are chosen three to be tested. Each two students can be taken in such triple only once. Prove that for the greatest $k$ satisfying these conditions, the following inequalities are true: $\frac{n(n-3)}{6}\leq k\leq \frac{n(n-1)}{6}$.

2003 German National Olympiad, 6
Tags: coprime , divisibility , pairs , infinitely many solutions , number theory
Prove that there are infinitely many coprime, positive integers $a,b$ such that $a$ divides $b^2 -5$ and $b$ divides $a^2 -5.$