2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/128314Let G be a finite Abelian group and A be a subset G\times G of cardinality at least |G|^2/(log log |G|)^c, where c>0 is an absolute constant. We prove that A contains a triple {(k,m), (k+d,m), (k,m+d)}, where d does not equal 0. This theorem is a two-dimensional generalization of Szemeredi's theorem on arithmetic progressions.40 pagesNumber TheoryCombinatoricstext