2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64802We prove that if one has k non-intersecting arithmetic progressions of integers, with common differences 2 <= q_1,...,q_k <= x, then k < x exp((-1/6 + o(1)) sqrt(log x loglog x)). This improves a result of Szemeredi and Erdos.SubmittedCombinatoricsNumber Theory05D99text