New congruences for the Bernoulli numbers-Reference-Cited by-同舟云学术

New congruences for the Bernoulli numbers

Published:1987 Issue:177 Volume:48 Page:341-350
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Tanner Jonathan W.,Wagstaff Samuel S.

Abstract

We prove a new congruence for computing Bernoulli numbers modulo a prime. Since it is similar to Vandiver’s congruences but has fewer terms, it may be used to test primes for regularity efficiently. We have programmed this test on a CYBER 205 computer. Fermat’s "Last Theorem" has been proved for all exponents up to 150000.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/1987-48-177/S0025-5718-1987-0866120-4/S0025-5718-1987-0866120-4.pdf

Reference6 articles.

1. R. W. Hockney & C. R. Jesshope, Parallel Computers: Architecture, Programming and Algorithms, Adam Hilger, Bristol, 1981.

2. 𝑝-adic proofs of congruences for the Bernoulli numbers;Johnson, Wells;J. Number Theory,1975

3. Lacunary recurrence formulas for the numbers of Bernoulli and Euler;Lehmer, D. H.;Ann. of Math. (2),1935

4. Jonathan W. Tanner, Proving Fermat’s Last Theorem for Many Exponents by Computer, B. A. Thesis, Harvard University, 1985.

5. On Bernoulli’s numbers and Fermat’s last theorem;Vandiver, H. S.;Duke Math. J.,1937

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