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Minimal f(2007) for a functional equation

University · ●●●●○ 100 pts

Let ff be a function taking the positive integers to the positive integers, such that f(mf(n))=nf(m)f(mf(n)) = nf(m) for all positive integers mm and nn. Find the smallest possible value of f(2007)f(2007).

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multiplicative functionsprime factorisationdivisor function