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For every n\in\mathbb{N} let d(n) denote the number of (positive) divisors of n. Find all functions f: \mathbb{N}\to\mathbb{N} with the following properties: d\left(f(x)\right) = x for all x\in\mathbb{N}. f(xy) divides (x - 1)y^{xy - 1}f(x) for all x, y\in\mathbb{N}.

Proposed by Bruno Le Floch, France

Slični zadaci

#NaslovOznakeRj.KvalitetaTežina
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