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(a+ b)/gcd(a, b) \in M

Source: Switzerland - 2005 Swiss MO Final Round p4

December 26, 2022
number theorygreatest common divisorGCD

Problem Statement

Determine all sets MM of natural numbers such that for every two (not necessarily different) elements a,ba, b from MM , a+bgcd(a,b)\frac{a + b}{gcd(a, b)} lies in MM.
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