MathDB

N8

Part of 2015 Indonesia MO Shortlist

Problems(1)

infinite n such that exists naturals a,b: a + b = n and ab | n^2 + n + 1

Source: INAMO Shortlist 2015 N8

5/14/2019
The natural number nn is said to be good if there are natural numbers aa and bb that satisfy a+b=na + b = n and ab∣n2+n+1ab | n^2 + n + 1. (a) Show that there are infinitely many good numbers. (b) Show that if nn is a good number, then 7∤n7 \nmid n.
number theoryDiophantine Equationsinfinitely many solutionsIndonesia