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Benelux Couples

Source: Benelux Mathematical Olympiad 2011, Problem 1

May 7, 2011
number theory proposednumber theory

Problem Statement

An ordered pair of integers (m,n)(m,n) with 1<m<n1<m<n is said to be a Benelux couple if the following two conditions hold: mm has the same prime divisors as nn, and m+1m+1 has the same prime divisors as n+1n+1. (a) Find three Benelux couples (m,n)(m,n) with m⩽14m\leqslant 14. (b) Prove that there are infinitely many Benelux couples
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