MathDB
unique f if f(prime) = 1; f(ab) = a f(b) + f(a) b

Source: 2000 Swedish Mathematical Competition p5

March 21, 2021
functional equationfunctionalnumber theory

Problem Statement

Let f(n)f(n) be defined on the positive integers and satisfy: f(prime)=1f(prime) = 1, f(ab)=af(b)+f(a)bf(ab) = a f(b) + f(a) b. Show that ff is unique and find all nn such that n=f(n)n = f(n).
Back to ProblemsView on AoPS