MathDB

C1

Part of 2021 IMO Shortlist

Problems(1)

GCD and COMB

Source: 2021 ISL C1

7/12/2022
Let SS be an infinite set of positive integers, such that there exist four pairwise distinct a,b,c,d∈Sa,b,c,d \in S with gcd⁡(a,b)≠gcd⁡(c,d)\gcd(a,b) \neq \gcd(c,d). Prove that there exist three pairwise distinct x,y,z∈Sx,y,z \in S such that gcd⁡(x,y)=gcd⁡(y,z)≠gcd⁡(z,x)\gcd(x,y)=\gcd(y,z) \neq \gcd(z,x).
combinatorics