Some new kinds of pseudoprimes

Browkin, Jerzy

doi:10.1090/S0025-5718-03-01617-X

Some new kinds of pseudoprimes
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by Jerzy Browkin;

Math. Comp. 73 (2004), 1031-1037

DOI: https://doi.org/10.1090/S0025-5718-03-01617-X

Published electronically: August 20, 2003

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Erratum: Math. Comp. 74 (2005), 1573-1573.

Abstract:

We define some new kinds of pseudoprimes to several bases, which generalize strong pseudoprimes. We call them Sylow $p$-pseudoprimes and elementary Abelian $p$-pseudoprimes. It turns out that every $n<10^{12},$ which is a strong pseudoprime to bases 2, 3 and 5, is not a Sylow $p$-pseudoprime to two of these bases for an appropriate prime $p|n-1.$ We also give examples of strong pseudoprimes to many bases which are not Sylow $p$-pseudoprimes to two bases only, where $p=2$ or $3.$

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