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Aurifeuillian factorizations and the period of the Bell numbers modulo a prime |
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| Authors: | Samuel S. Wagstaff Jr.. |
| Affiliation: | Department of Computer Sciences, Purdue University, West Lafayette, Indiana 47907 |
| Abstract: | We show that the minimum period modulo  of the Bell exponential integers is  for all primes  and several larger  . Our proof of this result requires the prime factorization of these periods. For some primes  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. |
| Keywords: | Bell numbers period modulo $p$ integer factorization Lucas' identities Aurifeuillian factorization |
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