Problem

Source: 2012 Indonesia Round 2 TST 2 Problem 4

Tags: function, number theory unsolved, number theory



Let N be the set of positive integers. For every nN, define d(n) as the number of positive divisors of n. Find all functions f:NN such that: a) d(f(x))=x for all xN b) f(xy) divides (x1)yxy1f(x) for all x,yN