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af(bc)+bf(ac)+cf(ab)=(a+b+c)f(ab+bc+ac)

Source: 1st TASIMO Day2, Problem5

May 19, 2024
functional equationAlgebraic Number Theoryalgebra

Problem Statement

Find all functions f:Z+ā†’Z+f: \mathbb{Z^+} \to \mathbb{Z^+} such that for all integers a,b,ca, b, c we have af(bc)+bf(ac)+cf(ab)=(a+b+c)f(ab+bc+ac). af(bc)+bf(ac)+cf(ab)=(a+b+c)f(ab+bc+ac). Note. The set Z+\mathbb{Z^+} refers to the set of positive integers. Proposed by Mojtaba Zare, Iran
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