MathDB

3

Part of 2022 China Second Round A1

Problems(1)

the existence of a set...or not?

Source: 2022 China Second Round A1 P3

10/30/2022
Does there exist an infinite set SS consisted of positive integers,so that for any x,y,z,w∈S,x<y,z<wx,y,z,w\in S,x<y,z<w,if (x,y)≠(z,w)(x,y)\ne (z,w),then gcd⁡(xy+2022,zw+2022)=1\gcd(xy+2022,zw+2022)=1?
number theory