The period of the Bell numbers modulo a prime

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Author

Peter Montgomery, Sangil Nahm, Samuel Wagstaff Jr

Tech report number

CERIAS TR 2010-01

Entry type

article

Abstract

We discuss the number in the title, especially whether the minimum period of the Bell numbers modulo p can be a proper divisor of N_p = (p^p-1)/(p-1). The investigation leads to interesting new theorems about possible prime factors of N_p. For example, we show that if p -s odd and q = 4m^2p+1 is prime and m is a positive integer, then q divides p^{m^2p} - 1. Then we explain how this fact influences the probability that q divides N_p

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Date

2010 – 1 – 1

Institution

Purdue University

Journal

Math Comp

Key alpha

Wagstaff

Affiliation

CERIAS and Computer Science

Publication Date

2010-01-01

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