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f(xy) = f(x)+ f(y)+k f(gcd(x,y)) , f(1995) =1996

Source: Czech And Slovak Mathematical Olympiad, Round III, Category A 1996 p5

February 20, 2020
functionalfunctional equationalgebra

Problem Statement

For which integers kk does there exist a function f:N→Zf : N \to Z such that f(1995)=1996f(1995) =1996 and f(xy)=f(x)+f(y)+kf(gcd(x,y))f(xy) = f(x)+ f(y)+k f(gcd(x,y)) for all x,y∈Nx,y \in N?
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