IMO 2008 Shortlist N5
For every n ∈ N let d(n) denote the number of (positive) divisors of n. Find all func- tions f : N → N with the followin...
Category: Number Theory
Problem
For every n ∈ N let d(n) denote the number of (positive) divisors of n. Find all func- tions f : N → N with the following properties: (i) d(f(x)) = x for all x ∈ N; (ii) f(xy) divides (x − 1)yxy−1 f(x) for all x,y ∈ N.