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Interesting NT Problem That Looks Like 2020 IMO P5

Source: 2021 Taiwan TST Round 2 Independent Study 1-N

April 7, 2021
number theoryTaiwan

Problem Statement

Let SS be a set of positive integers such that for every a,b∈Sa,b\in S, there always exists c∈Sc\in S such that c2c^2 divides a(a+b)a(a+b). Show that there exists an a∈Sa\in S such that aa divides every element of SS.
Proposed by usjl
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