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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



New congruences for the Bernoulli numbers

Authors: Jonathan W. Tanner and Samuel S. Wagstaff
Journal: Math. Comp. 48 (1987), 341-350
MSC: Primary 11B68; Secondary 11D41, 11Y50
MathSciNet review: 866120
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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.

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Keywords: Bernoulli numbers, Vandiver's congruence, Fermat's "Last Theorem"
Article copyright: © Copyright 1987 American Mathematical Society