Skip to content
DSML.KZ
Publications

Article · Proceedings of the Japan Academy Series A Mathematical Sciences · October 5, 2022

Euler tangent numbers modulo 720 and Genocchi numbers modulo 45

Askar Serkulovich Dzhumadil'daev, Medet Jumadildayev

Medet Jumadildayev
Open via DOIPDF

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.

Advanced Mathematical IdentitiesAdvanced Combinatorial MathematicsMathematical functions and polynomialsGenocchi numbersEuler polynomialscongruences

More by Medet Jumadildayev