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Existence of function on a set

Source: APMO 2015 Problem 2

March 30, 2015
functionalgebra

Problem Statement

Let S={2,3,4,…}S = \{2, 3, 4, \ldots\} denote the set of integers that are greater than or equal to 22. Does there exist a function f:S→Sf : S \to S such that f(a)f(b)=f(a2b2) for all a,b∈S with a≠b?f (a)f (b) = f (a^2 b^2 )\text{ for all }a, b \in S\text{ with }a \ne b?
Proposed by Angelo Di Pasquale, Australia
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