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Find all Z → Z functions - [UKRMO 2009 Grade 11]

Source:

January 23, 2011
functionabsolute valuealgebra proposedalgebra

Problem Statement

Find all functions f:Z→Zf : \mathbb Z \to \mathbb Z such that f(n∣m∣)+f(n(∣m∣+2))=2f(n(∣m∣+1))∀m,n∈Z.f (n |m|) + f (n(|m| +2)) = 2f (n(|m| +1)) \qquad \forall m,n \in \mathbb Z.
Note. ∣x∣|x| denotes the absolute value of the integer x.x.
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