Problem

Source: IMO 2015 Shortlist, N8

Tags: inequalities, number theory, prime factorization, function, IMO Shortlist



For every positive integer n with prime factorization n=ki=1pαii, define (n)=i:pi>10100αi.That is, (n) is the number of prime factors of n greater than 10100, counted with multiplicity. Find all strictly increasing functions f:ZZ such that (f(a)f(b))(ab)for all integers a and b with a>b. Proposed by Rodrigo Sanches Angelo, Brazil