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

2025 Bulgarian Winter Tournament, 12.3
Tags: function , number theory , sequence , divisibility , large number , polynomial
Determine all functions $f: \mathbb{Z}_{\geq 2025} \to \mathbb{Z}_{>0}$ such that $mn+1$ divides $f(m)f(n) + 1$ for any integers $m,n \geq 2025$ and there exists a polynomial $P$ with integer coefficients, such that $f(n) \leq P(n)$ for all $n\geq 2025$.

2015 NIMO Summer Contest, 8
Tags: number theory , prime , exponent , large number
It is given that the number $4^{11}+1$ is divisible by some prime greater than $1000$. Determine this prime. [i] Proposed by David Altizio [/i]