IMO 2010 Shortlist N4
Let a,b be integers, and let Ppxqax3 bx. For any positive integer n we say that the pair pa,bq is n-good if n Ppmq...
Category: Number Theory
Problem
Let a,b be integers, and let Ppxqax3 bx. For any positive integer n we say that the pair pa,bq is n-good if n PpmqPpkq implies n m k for all integers m,k. We say that pa,bq is very good if pa,bq is n-good for infinitely many positive integers n. (a) Find a pair pa,bq which is 51-good, but not very good. (b) Show that all 2010-good pairs are very good. (Turkey)