Open Access
October 2022 Euler tangent numbers modulo 720 and Genocchi numbers modulo 45
Askar Dzhumadil’daev, Medet Jumadildayev
Proc. Japan Acad. Ser. A Math. Sci. 98(8): 63-66 (October 2022). DOI: 10.3792/pjaa.98.012

Abstract

We establish congruences for higher order Euler polynomials modulo 720. We apply this result for constructing analogues of Stern congruences for Euler secant numbers $E_{4n}\equiv 5(\mathrm{mod}\ 60), E_{4n+2}\equiv -1(\mathrm{mod}\ 60)$ to Euler tangent numbers and Genocchi numbers. We prove that Euler tangent numbers satisfy the following congruences $E_{4n+1}\equiv 16(\mathrm{mod}\ 720)$, and $E_{4n+3}\equiv -272(\mathrm{mod}\ 720)$. We establish 12-periodic property of Genocchi numbers modulo 45.

Citation

Download Citation

Askar Dzhumadil’daev. Medet Jumadildayev. "Euler tangent numbers modulo 720 and Genocchi numbers modulo 45." Proc. Japan Acad. Ser. A Math. Sci. 98 (8) 63 - 66, October 2022. https://doi.org/10.3792/pjaa.98.012

Information

Published: October 2022
First available in Project Euclid: 29 September 2022

MathSciNet: MR4492079
zbMATH: 1510.11077
Digital Object Identifier: 10.3792/pjaa.98.012

Subjects:
Primary: 11B68

Keywords: Genocchi numbers , Higher-order Euler numbers , Ramanujan congruences , secant numbers , tangent numbers

Rights: Copyright © 2022 The Japan Academy

Vol.98 • No. 8 • October 2022
Back to Top