2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76454The generalized Euler number E_{n|k} counts the number of permutations of {1,2,...,n} which have a descent in position m if and only if m is divisible by k. The classical Euler numbers are the special case when k=2. In this paper, we study divisibility properties of a q-analog of E_{n|k}. In particular, we generalize two theorems of Andrews and Gessel about factors of the q-tangent numbers.9 pages, 0 figures, Latex, see related papers at http://www.math.msu.edu/~saganCombinatorics11B68 (Primary) 11A07, 11B65, 05A30 (Secondary)text