A new approach to congruences of Kummer type for Bernoulli numbers

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Abstract

By means of simple identities among rational functions of a particular type, we are able to produce identities among Bernoulli numbers and from them congruences of the form.

when the odd prime p has the property that p-1 is not a divisor of the positive even integer m. With such relations, we are able to produce new identities among Bernoulli numbers as well as reproving congruences of Kummer type such as

when ω is a multiple of (p-1)pe-1,  e ≥ 1.

 

  • Minking Eie Department of Mathematics, National Chung Cheng University, Ming-Hsiung, Chia-Yi 621, Taiwan.
  • Yao Lin Ong Department of Mathematics, National Chung Cheng University, Ming-Hsiung, Chia-Yi 621, Taiwan.
  • Pages: 289 - 304
  • Date Published: 2003-06-01
  • Vol. 5 No. 2 (2003): CUBO, Matemática Educacional

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Published

2003-06-01

How to Cite

[1]
M. Eie and Y. Lin Ong, “A new approach to congruences of Kummer type for Bernoulli numbers”, CUBO, vol. 5, no. 2, pp. 289–304, Jun. 2003.

Issue

Vol. 5 No. 2 (2003): CUBO, Matemática Educacional

Section

Articles