IMO 2015 Shortlist N8
For every positive integer n with prime factorization n “ śk i“1 pαi i , define ℧pnq “ ÿ i: pią10100 αi. That is, ℧pnq i...
Category: Number Theory
Problem
For every positive integer n with prime factorization n “ śk i“1 pαi i , define ℧pnq “ ÿ i: pią10100 αi. That is, ℧pnq is the number of prime factors of n greater than 10100 , counted with multiplicity. Find all strictly increasing functions f : Z Ñ Z such that ℧ ` fpaq ´ fpbq ˘ ď ℧pa ´ bq for all integers a and b with a ą b. (Brazil) 8 IMO 2015 Thailand