欧拉正切数以720为模，格诺奇数以45为模

Pub Date : 2022-10-11 DOI:10.3792/pjaa.98.012

A. Dzhumadil'daev, Medet Jumadildayev

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引用次数: 0

摘要

我们建立了以720为模的高阶欧拉多项式的同余式。我们将这一结果应用于构造欧拉正割数e4 n (cid:3) 5 ð mod 60 Þ的Stern同余的类似物;e4n þ 2 (cid:3) (cid:4) 1 ð mod 60 Þ到Euler正切数和Genocchi数。我们证明了欧拉正切数满足下列同余式e4n þ 1 (cid:3) 16 ð mod 720 Þ和e4n þ 3 (cid:3) (cid:4) 272 ð mod 720 Þ。建立了以45为模的Genocchi数的12周期性质。

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Euler tangent numbers modulo 720 and Genocchi numbers modulo 45

: 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 4 n (cid:3) 5 ð mod 60 Þ ; E 4 n þ 2 (cid:3) (cid:4) 1 ð mod 60 Þ to Euler tangent numbers and Genocchi numbers. We prove that Euler tangent numbers satisfy the following congruences E 4 n þ 1 (cid:3) 16 ð mod 720 Þ , and E 4 n þ 3 (cid:3) (cid:4) 272 ð mod 720 Þ . We establish 12-periodic property of Genocchi numbers modulo 45.

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