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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