2

Part of 2008 Romanian Master of Mathematics

Problems(1)

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

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

Prove that every bijective function

f: \mathbb{Z}\rightarrow\mathbb{Z}

can be written in the way f\equal{}u\plus{}v where

u,v: \mathbb{Z}\rightarrow\mathbb{Z}

are bijective functions.

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