Some Congruences for Generalized Euler Numbers

Abstract

The generalized Euler numbers may be defined bySince 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 isThey also proved that , and , and they made several conjectures which may be stated as follows:C1C2C3C4