Let N be the set of positive integers. For every n∈N, define d(n) as the number of positive divisors of n. Find all functions f:N→N such that: a) d(f(x))=x for all x∈N b) f(xy) divides (x−1)yxy−1f(x) for all x,y∈N
Problem
Source: 2012 Indonesia Round 2 TST 2 Problem 4
Tags: function, number theory unsolved, number theory