MathDB

14

Part of 2004 Iran MO (3rd Round)

Problems(1)

easy one

Source: iran2004(number theory exam)

9/11/2004
We define f:Nā†’N f: \mathbb{N} \rightarrow \mathbb{N}, f(n) \equal{} \sum_{k \equal{} 1}^{n}(k,n). a) Show that if \gcd(m,n)\equal{}1 then we have f(mn)\equal{}f(m)\cdot f(n); b) Show that \sum_{d|n}f(d) \equal{} nd(n).
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