MathDB
Existence of a good pair

Source: Indonesian MO (INAMO) 2009, Day 2, Problem 7

August 8, 2009
number theoryrelatively primemodular arithmeticnumber theory unsolved

Problem Statement

A pair of integers (m,n) (m,n) is called good if m\mid n^2 \plus{} n \ \text{and} \ n\mid m^2 \plus{} m Given 2 positive integers a,b>1 a,b > 1 which are relatively prime, prove that there exists a good pair (m,n) (m,n) with a∣m a\mid m and b∣n b\mid n, but a∤n a\nmid n and b∤m b\nmid m.
Back to ProblemsView on AoPS