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Functional equation on rational numbers

Source: Romanian IMO TST 2006, day 4, problem 1

May 19, 2006
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Problem Statement

Let rr and ss be two rational numbers. Find all functions f:Q→Qf: \mathbb Q \to \mathbb Q such that for all x,y∈Qx,y\in\mathbb Q we have f(x+f(y))=f(x+r)+y+s. f(x+f(y)) = f(x+r)+y+s.
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