MathDB
$p|f(m+n) \iff p|f(m) + f(n)$ (IMO Shortlist 2007, N5)

Source: IMO Shortlist 2007, N5, AIMO 2008, TST 3, P3

July 13, 2008
functionmodular arithmeticnumber theoryDivisibilityIMO Shortlist

Problem Statement

Find all surjective functions f:N→N f: \mathbb{N} \to \mathbb{N} such that for every m,n∈N m,n \in \mathbb{N} and every prime p, p, the number f(m+n) f(m + n) is divisible by p p if and only if f(m)+f(n) f(m) + f(n) is divisible by p p.
Author: Mohsen Jamaali and Nima Ahmadi Pour Anari, Iran
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