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A certain magma of natural numbers

Source:

December 13, 2019
algebraabstract algebraDivisibilitynumber theory

Problem Statement

Determine all sets of natural numbers A A that have at least two elements, and satisfying the following proposition: \forall x,y\in A  x>y\implies \frac{x-y}{\text{gcd} (x,y)} \in A.
Marius Perianu