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Mathematics of Computation

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$ p$-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.

References [Enhancements On Off] (What's this?)

  • [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 $ Q({\mu _p})$,'' 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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Keywords: Bernoulli numbers, p-divisibility
Article copyright: © Copyright 1980 American Mathematical Society

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