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f ,g : Z -> Z, f (g(x)+y) = g( f (y)+x) , g 1-1

Source: Czech and Slovak Match 1995 P2

October 1, 2017
functional equation in Zalgebra

Problem Statement

Find all pairs of functions f,g:Zā†’Zf ,g : Z \rightarrow Z that satisfy f(g(x)+y)=g(f(y)+x)f (g(x)+y) = g( f (y)+x) for all integers x,y x,y and such that g(x)=g(y)g(x) = g(y) only if x=yx = y.
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