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f(n + m) =f(n)f(m) from m,n integers >=1

Source: III - Rioplatense 1993 L3 P1

September 19, 2022
number theoryfunctionalfunctional equation

Problem Statement

Find all functions ff defined on the integers greater than or equal to 11 that satisfy: (a) for all n,f(n)n,f(n) is a positive integer. (b) f(n+m)=f(n)f(m)f(n + m) =f(n)f(m) for all mm and nn. (c) There exists n0n_0 such that f(f(n0))=[f(n0)]2f(f(n_0)) = [f(n_0)]^2 .
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