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France TST 2000 D1Q2

Source:

March 2, 2013
functionnumber theory unsolvednumber theory

Problem Statement

A function from the positive integers to the positive integers satisfies these properties 1. f(ab)=f(a)f(b)f(ab)=f(a)f(b) for any two coprime positive integers a,ba,b. 2. f(p+q)=f(p)+f(q)f(p+q)=f(p)+f(q) for any two primes p,qp,q. Prove that f(2)=2,f(3)=3,f(1999)=1999f(2)=2, f(3)=3, f(1999)=1999.
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