2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76518This is a contribution to the number theory of the dimer problem. The number of dimer coverings (i.e., perfect matchings) of a square lattice graph is discussed modulo powers of 2.8 pages, LaTeX. Submitted to Discrete MathematicsCombinatorics05B45(Primary);05A15;05C70(Secondary)text