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Function acting on a,b, and gcd(a,b)

Source: Baltic Way 2001

November 17, 2010
functionalgebra proposedalgebra

Problem Statement

The real-valued function ff is defined for all positive integers. For any integers a>1,b>1a>1, b>1 with d=gcd⁡(a,b)d=\gcd (a, b), we have f(ab)=f(d)(f(ad)+f(bd))f(ab)=f(d)\left(f\left(\frac{a}{d}\right)+f\left(\frac{b}{d}\right)\right) Determine all possible values of f(2001)f(2001).
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