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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Pseudoprimes for higher-order linear recurrence sequences

Author: S. Gurak
Journal: Math. Comp. 55 (1990), 783-813
MSC: Primary 11Y11; Secondary 11A51, 11B37, 11B50
MathSciNet review: 1035934
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Abstract: With the advent of high-speed computing, there is a rekindled interest in the problem of determining when a given whole number $ N > 1$ is prime or composite. While complex algorithms have been developed to settle this for 200-digit numbers in a matter of minutes with a supercomputer, there is a need for simpler, more practical algorithms for dealing with numbers of a more modest size. Such practical tests for primality have recently been given (running in deterministic linear time) in terms of pseudoprimes for certain second- or third-order linear recurrence sequences. Here, a powerful general theory is described to characterize pseudoprimes for higher-order recurrence sequences. This characterization leads to a broadening and strengthening of practical primality tests based on such pseudoprimes.

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Article copyright: © Copyright 1990 American Mathematical Society