-divisibility of certain sets of Bernoulli numbers

Author:
Samuel S. Wagstaff

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

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Abstract | References | Similar Articles | Additional Information

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]**E. LEHMER, ``On congruences involving Bernoulli numbers and the quotients of Fermat and Wilson,''*Ann. of Math.*, v. 39, 1938, pp. 350-360. MR**1503412****[2]**K. RIBET, ``A modular construction of unramified*p*-extensions of ,''*Invent. Math.*, v. 34, 1976, pp. 151-162. MR**0419403 (54:7424)****[3]**S. V. ULLOM, ``Upper bounds for*p*-divisibility of sets of Bernoulli numbers,''*J. Number Theory.*(To appear.) MR**578812 (81h:10019)****[4]**S. S. WAGSTAFF, JR., ``The irregular primes to 125000,''*Math. Comp.*, v. 32, 1978, pp. 583-591. MR**58**#10711. MR**0491465 (58:10711)**

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

Keywords:
Bernoulli numbers,
*p*-divisibility

Article copyright:
© Copyright 1980
American Mathematical Society