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

Source: INAMO Shortlist 2015 N8

May 14, 2019
number theoryDiophantine Equationsinfinitely many solutionsIndonesia

Problem Statement

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.
Back to ProblemsView on AoPS