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Found problems: 1

2001 Romania Team Selection Test, 1
Tags: polynomial congruence , modular arithmetic , number theory
Find all pairs $\left(m,n\right)$ of positive integers, with $m,n\geq2$, such that $a^n-1$ is divisible by $m$ for each $a\in \left\{1,2,3,\ldots,n\right\}$.