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functional equation on integers with divisibility

Source: MEMO 2016 I4

August 24, 2016
number theorynumber theory proposedfunctional equationfunctionDivisibilityalgebra

Problem Statement

Find all f:N→Nf : \mathbb{N} \to \mathbb{N} such that f(a)+f(b)f(a) + f(b) divides 2(a+b−1)2(a + b - 1) for all a,b∈Na, b \in \mathbb{N}.
Remark: N={1,2,3,…}\mathbb{N} = \{ 1, 2, 3, \ldots \} denotes the set of the positive integers.
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