Problem

Source: INAMO Shortlist 2015 N8

Tags: number theory, Diophantine Equations, infinitely many solutions, Indonesia



The natural number n is said to be good if there are natural numbers a and b that satisfy a+b=n and ab|n2+n+1. (a) Show that there are infinitely many good numbers. (b) Show that if n is a good number, then 7.