olymmath

CAPS 1995 Problem 2

    Find all pairs of functions f,g:Z→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,yx,y and such that g(x)=g(y)g(x) = g(y) only if x=yx = y .

    Dataset text AI-MO AoPS. Quoted with source.

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