Problem

Source: Cono Sur Olympiad 2016, problem 6

Tags: number theory, cono sur



We say that three different integers are friendly if one of them divides the product of the other two. Let n be a positive integer. a) Show that, between n2 and n2+n, exclusive, does not exist any triplet of friendly numbers. b) Determine if for each n exists a triplet of friendly numbers between n2 and n2+n+3n , exclusive.