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Find all functions

Source: 2012 China TST- Quiz 1 - Day 2 -P6

March 15, 2012
functiongroup theoryabstract algebrafloor functioninductionalgebra proposedalgebra

Problem Statement

nn being a given integer, find all functions f ⁣:Z→Zf\colon \mathbb{Z} \to \mathbb{Z}, such that for all integers x,yx,y we have f(x+y+f(y))=f(x)+nyf\left( {x + y + f(y)} \right) = f(x) + ny.
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