About the period of bell numbers modulo a prime

Mireille Car; Luis H. Gallardo; Olivier Rahavandrainy; Leonid N. Vaserstein

doi:10.4134/BKMS.2008.45.1.143

About the period of bell numbers modulo a prime

Mireille Car
, Luis H. Gallardo
, Olivier Rahavandrainy
, Leonid N. Vaserstein

Mathematics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

Let p be a prime number. It is known that the order o(r) of a root r of the irreducible polynomial x^p - x - 1 over F_p divides g(p) = p^p-1/p-1 Samuel Wagstaff recently conjectured that o(r) = g(p) for any prime p. The main object of the paper is to give some subsets S of {1,...,g(p)} that do not contain o(r).

Original language	English (US)
Pages (from-to)	143-155
Number of pages	13
Journal	Bulletin of the Korean Mathematical Society
Volume	45
Issue number	1
DOIs	https://doi.org/10.4134/BKMS.2008.45.1.143
State	Published - Feb 2008

All Science Journal Classification (ASJC) codes

General Mathematics

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10.4134/BKMS.2008.45.1.143

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abstract = "Let p be a prime number. It is known that the order o(r) of a root r of the irreducible polynomial xp - x - 1 over Fp divides g(p) = pp-1/p-1 Samuel Wagstaff recently conjectured that o(r) = g(p) for any prime p. The main object of the paper is to give some subsets S of \{1,...,g(p)\} that do not contain o(r).",

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AU - Car, Mireille

AU - Gallardo, Luis H.

AU - Rahavandrainy, Olivier

AU - Vaserstein, Leonid N.

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Y1 - 2008/2

N2 - Let p be a prime number. It is known that the order o(r) of a root r of the irreducible polynomial xp - x - 1 over Fp divides g(p) = pp-1/p-1 Samuel Wagstaff recently conjectured that o(r) = g(p) for any prime p. The main object of the paper is to give some subsets S of {1,...,g(p)} that do not contain o(r).

AB - Let p be a prime number. It is known that the order o(r) of a root r of the irreducible polynomial xp - x - 1 over Fp divides g(p) = pp-1/p-1 Samuel Wagstaff recently conjectured that o(r) = g(p) for any prime p. The main object of the paper is to give some subsets S of {1,...,g(p)} that do not contain o(r).

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M3 - Article

AN - SCOPUS:40749126779

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JF - Bulletin of the Korean Mathematical Society

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About the period of bell numbers modulo a prime

Abstract

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