欧拉正切数以720为模，格诺奇数以45为模

IF 0.4 4区数学 Q4 MATHEMATICS

Proceedings of the Japan Academy Series A-Mathematical Sciences 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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来源期刊

Proceedings of the Japan Academy Series A-Mathematical Sciences 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： The aim of the Proceedings of the Japan Academy, Series A, is the rapid publication of original papers in mathematical sciences. The paper should be written in English or French (preferably in English), and at most 6 pages long when published. A paper that is a résumé or an announcement (i.e. one whose details are to be published elsewhere) can also be submitted. The paper is published promptly if once communicated by a Member of the Academy at its General Meeting, which is held monthly except in July and in August.