$p$-divisibility of certain sets of Bernoulli numbers
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- by Samuel S. Wagstaff PDF
- Math. Comp. 34 (1980), 647-649 Request permission
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.References
- 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, DOI 10.2307/1968791
- Kenneth A. Ribet, A modular construction of unramified $p$-extensions of $Q(\mu _{p})$, Invent. Math. 34 (1976), no. 3, 151–162. MR 419403, DOI 10.1007/BF01403065
- Stephen V. Ullom, Upper bounds for $p$-divisibility of sets of Bernoulli numbers, J. Number Theory 12 (1980), no. 2, 197–200. MR 578812, DOI 10.1016/0022-314X(80)90053-0
- Samuel S. Wagstaff Jr., The irregular primes to $125000$, Math. Comp. 32 (1978), no. 142, 583–591. MR 491465, DOI 10.1090/S0025-5718-1978-0491465-4
Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Math. Comp. 34 (1980), 647-649
- MSC: Primary 10A40; Secondary 12A50
- DOI: https://doi.org/10.1090/S0025-5718-1980-0559208-2
- MathSciNet review: 559208