help me in solving the question in attachment

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- Oct 20th 2013, 11:47 AMvirebbala90number theory
help me in solving the question in attachment

- Oct 20th 2013, 01:00 PMSlipEternalRe: number theory
Show it is true when $\displaystyle n$ is a prime power. Then use induction. Prove it is true for n=1, then assume it is true for all numbers up to n. If n+1 is a prime power, you already proved it is true. Otherwise, use the fact that f(n+1) = f(a)f(b) where b is a prime power, a and b are coprime, and ab=n+1. Both a and b will therefore be less than n, so you can apply the induction hypothesis.