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

Tags were heavily modified to better represent problems.

AND
OR
NO

Found problems: 1

2024 Rioplatense Mathematical Olympiad, 3
Let $a$, $b$, $c$ be positive integers. Prove that for infinitely many positive odd integers $n$, there exists an integer $m > n$ such that $a^n + b^n + c^n$ divides $a^m + b^m + c^m$.
tn number theory rioplatense inequalities modular arithmetic