IMO 2021 Shortlist A6

Let A be a finite set of (not necessarily positive) integers, and let m ě2 be an integer. Assume that there exist non-em...

IMO 2021 Shortlist A6

Category: Algebra

Problem

Let A be a finite set of (not necessarily positive) integers, and let m ě2 be an integer. Assume that there exist non-empty subsets B1,B2,B3,...,Bm of A whose elements add up to the sums m1 ,m2 ,m3 ,...,mm , respectively. Prove that A contains at least m{2 elements.