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rad(f(a)f(b)+f(b)f(c)+f(c)f(a))=rad(ab+bc+ca)

Source: Malaysian IMO TST 2022 P5

May 13, 2022
number theory

Problem Statement

Find all functions f:Z→Zf : \mathbb{Z}\rightarrow \mathbb{Z} such that for all prime pp the following condition holds: p∣ab+bc+ca  ⟺  p∣f(a)f(b)+f(b)f(c)+f(c)f(a)p \mid ab + bc + ca \iff p \mid f(a)f(b) + f(b)f(c) + f(c)f(a)
Proposed by Anzo Teh Zhao Yang
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