-divisibility of certain sets of Bernoulli numbers

Author:
Samuel S. Wagstaff

Journal:
Math. Comp. **34** (1980), 647-649

MSC:
Primary 10A40; Secondary 12A50

MathSciNet review:
559208

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Abstract: Recently, Ullom has proved an upper bound on the number of Bernoulli numbers in certain sets which are divisible by a given prime. We report on a search for such Bernoulli numbers and primes up to 1000000.

**[1]**Emma Lehmer,*On congruences involving Bernoulli numbers and the quotients of Fermat and Wilson*, Ann. of Math. (2)**39**(1938), no. 2, 350–360. MR**1503412**, 10.2307/1968791**[2]**Kenneth A. Ribet,*A modular construction of unramified 𝑝-extensions of𝑄(𝜇_{𝑝})*, Invent. Math.**34**(1976), no. 3, 151–162. MR**0419403****[3]**Stephen V. Ullom,*Upper bounds for 𝑝-divisibility of sets of Bernoulli numbers*, J. Number Theory**12**(1980), no. 2, 197–200. MR**578812**, 10.1016/0022-314X(80)90053-0**[4]**Samuel S. Wagstaff Jr.,*The irregular primes to 125000*, Math. Comp.**32**(1978), no. 142, 583–591. MR**0491465**, 10.1090/S0025-5718-1978-0491465-4

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DOI:
http://dx.doi.org/10.1090/S0025-5718-1980-0559208-2

Keywords:
Bernoulli numbers,
*p*-divisibility

Article copyright:
© Copyright 1980
American Mathematical Society