2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72741To determine Euler numbers modulo powers of two seems to be a difficult task. In this paper we achieve this and apply the explicit congruence to give a new proof of a classical result due to M. A. Stern.9 pages, to appear in J. Number TheoryNumber TheoryCombinatorics11B68; 11A07; 11S05text