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Mathematics of Computation

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Frobenius pseudoprimes

Author: Jon Grantham
Journal: Math. Comp. 70 (2001), 873-891
MSC (2000): Primary 11Y11
Published electronically: March 1, 2000
MathSciNet review: 1680879
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Abstract: The proliferation of probable prime tests in recent years has produced a plethora of definitions with the word “pseudoprime” in them. Examples include pseudoprimes, Euler pseudoprimes, strong pseudoprimes, Lucas pseudoprimes, strong Lucas pseudoprimes, extra strong Lucas pseudoprimes and Perrin pseudoprimes. Though these tests represent a wealth of ideas, they exist as a hodge-podge of definitions rather than as examples of a more general theory. It is the goal of this paper to present a way of viewing many of these tests as special cases of a general principle, as well as to re-formulate them in the context of finite fields. One aim of the reformulation is to enable the creation of stronger tests; another is to aid in proving results about large classes of pseudoprimes.

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Additional Information

Jon Grantham
Affiliation: Institute for Defense Analyses, Center for Computing Sciences, 17100 Science Drive, Bowie, MD 20715

Received by editor(s): January 6, 1998
Received by editor(s) in revised form: March 29, 1999
Published electronically: March 1, 2000
Article copyright: © Copyright 2000 American Mathematical Society