Some Congruences for Generalized Euler Numbers

Abstract

The generalized Euler numbers may be defined by Since is zero unless m divides n, we shall write for . Leeming and MacLeod [12] recently gave some congruences for these numbers. They found congruences (mod 16) for where m = 3, 6, 8, 12, and 16. Thus for m = 3, their congruence is They also proved that , and , and they made several conjectures which may be stated as follows: C1 C2 C3 C4