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Bijective function on Z is sum of 2 bijective functions on Z

Source: 1st Romanian Master in Mathematics (RMIM) 2008, Bucharest, Problem 2

February 9, 2008
functionalgorithmabsolute valuealgebra proposedalgebra

Problem Statement

Prove that every bijective function f:Z→Z f: \mathbb{Z}\rightarrow\mathbb{Z} can be written in the way f\equal{}u\plus{}v where u,v:Z→Z u,v: \mathbb{Z}\rightarrow\mathbb{Z} are bijective functions.
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