2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/126401We extend two well-known results in additive number theory, Sárközy's theorem on square differences in dense sets and a theorem of Green on long arithmetic progressions in sumsets, to subsets of random sets of asymptotic density 0. Our proofs rely on a restriction-type Fourier analytic argument of Green and Green-Tao.22 pagesNumber TheoryCombinatoricstext