Euler tangent numbers modulo 720 and Genocchi numbers modulo 45
Dzhumadil’Daev A. Jumadildayev M.
2022Japan Academy
Proceedings of the Japan Academy Series A: Mathematical Sciences
2022#98Issue 863 - 66 pp.
We establish congruences for higher order Euler polynomials modulo 720. We apply this result for constructing analogues of Stern congruences for Euler secant numbers E4n ≡ 5(mod 60), E4n+2 ≡ -1(mod 60) to Euler tangent numbers and Genocchi numbers.We prove that Euler tangent numbers satisfy the following congruences E4n+1 ≡ 16(mod 720), and E4n+3 ≡ -272(mod 720). We establish 12-periodic property of Genocchi numbers modulo 45
Genocchi numbers , Higher-order euler numbers , Ramanujan congruences , Secant numbers , Tangent numbers
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Kazakh-British Technical University, Tole bi 59, Almaty, 050000, Kazakhstan
Nazarbayev Intellectual School of Physics and Mathematics, 145 Zhamakayev Street, Almaty, 050000, Kazakhstan
Kazakh-British Technical University
Nazarbayev Intellectual School of Physics and Mathematics
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