IMO 2021 Shortlist C1
Let S be an infiniteset of positive integers, such that there exist four pairwise distinct a,b,c,d PS with gcdpa,bq‰gcdp...
Category: Combinatorics
Problem
Let S be an infiniteset of positive integers, such that there exist four pairwise distinct a,b,c,d PS with gcdpa,bq‰gcdpc,dq. Prove that there exist three pairwise distinct x,y,z PS such that gcdpx,yq“gcdpy,zq‰gcdpz,xq.