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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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Aurifeuillian factorizations and the period of the Bell numbers modulo a prime
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by Samuel S. Wagstaff Jr. PDF
Math. Comp. 65 (1996), 383-391 Request permission


We show that the minimum period modulo $p$ of the Bell exponential integers is $(p^p-1)/(p-1)$ for all primes $p<102$ and several larger $p$. Our proof of this result requires the prime factorization of these periods. For some primes $p$ the factoring is aided by an algebraic formula called an Aurifeuillian factorization. We explain how the coefficients of the factors in these formulas may be computed.
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Additional Information
  • Samuel S. Wagstaff Jr.
  • MR Author ID: 179915
  • Email:
  • Received by editor(s): August 24, 1993
  • Received by editor(s) in revised form: January 26, 1995
  • Additional Notes: Some of the computing reported in this work was performed on a MasPar computer at Purdue University which was supported in part by NSF Infrastructure Grant CDA-9015696.
  • © Copyright 1996 American Mathematical Society
  • Journal: Math. Comp. 65 (1996), 383-391
  • MSC (1991): Primary 11--04, 11B73; Secondary 11Y05, 12--04, 12E10, 12Y05
  • DOI:
  • MathSciNet review: 1325876