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Super congruences and Euler numbers

✍ Scribed by Zhi-Wei Sun


Book ID
107348527
Publisher
SP Science China Press
Year
2011
Tongue
English
Weight
341 KB
Volume
54
Category
Article
ISSN
1674-7283

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πŸ“œ SIMILAR VOLUMES


Congruences involving Bernoulli and Eule
✍ Zhi-Hong Sun πŸ“‚ Article πŸ“… 2008 πŸ› Elsevier Science 🌐 English βš– 263 KB

Let [x] be the integral part of x. Let p > 5 be a prime. In the paper we mainly determine ) in terms of Euler and Bernoulli numbers. For example, we have where E n is the nth Euler number and B n is the nth Bernoulli number.

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We use properties of p-adic integrals and measures to obtain congruences for higher-order Bernoulli and Euler numbers and polynomials, as well as for certain generalizations and for Stirling numbers of the second kind. These congruences are analogues and generalizations of the usual Kummer congruenc

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✍ Takashi Agoh πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 100 KB

Let B m be the mth Bernoulli number in the even suffix notation and let q(a, n)=(a j(n) -1)/n be the Fermat-Euler quotient, where a, n \ 2 are relatively prime positive integers and j is the Euler totient function. The main purpose of this paper is to devise a certain congruence involving the Bernou

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