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Some Congruences for Generalized Euler Numbers

Published online by Cambridge University Press:  20 November 2018

Ira M. Gessel
Ira M. Gessel*
Affiliation:
Massachusetts Institute of Technology, Cambridge, Massachusetts
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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

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 35 , Issue 4 , 01 August 1983 , pp. 687 - 709
Copyright
Copyright © Canadian Mathematical Society 1983

References

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