N4

Part of 2024-IMOC

Problems(1)

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

Source: 2024IMOC

Given a set of integers

S

satisfies that: for any

a,b,c\in S

a,b,c

can be the same),

ab+c\in S

\\ Find all pairs of integers

(x,y)

x,y\in S

S=\mathbb{Z}