Problem

Source: Iran Third Round MO 1998, Exam 2, P1

Tags: function, number theory proposed, number theory



Find all functions f:NN such that for all positive integers m,n, (i) mf(f(m))=(f(m))2, (ii) If gcd, then f(mn) \cdot f(d)=d \cdot f(m) \cdot f(n), (iii) f(m)=m if and only if m=1.