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f(x+y) = f (x) f (y) for all x,y >= a with x + y >= a.

Source: Austrian Polish 1982 APMC

April 30, 2020
functionalfunctional equationalgebra

Problem Statement

An integer aa is given. Find all real-valued functions f(x)f (x) defined on integers x≥ax \ge a, satisfying the equation f(x+y)=f(x)f(y)f (x+y) = f (x) f (y) for all x,y≥ax,y \ge a with x+y≥ax + y \ge a.
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