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Mathematics of Computation

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Wilson quotients for composite moduli

Authors: Takashi Agoh, Karl Dilcher and Ladislav Skula
Journal: Math. Comp. 67 (1998), 843-861
MSC (1991): Primary 11A07; Secondary 11B68
MathSciNet review: 1464140
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Abstract: An analogue for composite moduli $m \geq 2$ of the Wilson quotient is studied. Various congruences are derived, and the question of when these quotients are divisible by $m$ is investigated; such an $m$ will be called a “Wilson number". It is shown that numbers in certain infinite classes cannot be Wilson numbers. Eight new Wilson numbers up to 500 million were found.

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Additional Information

Takashi Agoh
Affiliation: Department of Mathematics, Science University of Tokyo, Noda, Chiba 278, Japan

Karl Dilcher
Affiliation: Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, B3H 3J5, Canada

Ladislav Skula
Affiliation: Department of Mathematics, Faculty of Science, Masaryk University, 66295 Brno, Czech Republic

Received by editor(s): January 23, 1995
Received by editor(s) in revised form: May 22, 1996
Additional Notes: The first author was supported in part by a grant of the Ministry of Education, Science and Culture of Japan. The second author’s research was supported by NSERC of Canada. Research of the third author was supported by the Grant Agency of the Czech Republic, “Number Theory, its Algebraic Aspects and its Relationship to Computer Science", No. 201/93/2/22.
Article copyright: © Copyright 1998 American Mathematical Society