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a,b,c in S then ab+c in S

Source: 2024IMOC

August 1, 2024
number theory

Problem Statement

Given a set of integers SS satisfies that: for any a,b,c∈Sa,b,c\in S (a,b,ca,b,c can be the same), ab+c∈Sab+c\in S\\ Find all pairs of integers (x,y)(x,y) such that if x,y∈Sx,y\in S, then S=ZS=\mathbb{Z}.
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