Equivalence of Pepin's and the Lucas-Lehmer tests

Authors

  • John H. Jaroma Ave Maria University

Keywords:

Primes, primality test, Lehmer sequence, Pepin's test, Lucas-Lehmer test

Abstract

Pepin's test provides a necessary and sufficient condition for a Fermat number to be prime. The Lucas-Lehmer test does similarly for a Mersenne number. These tests share a common nature. However, this is evident neither by their usual statements nor their usual treatment in the literature. Furthermore, it is unusual to even find a proof of the latter result in elementary textbooks. The intent of this paper is to bring to light the equivalent structure of these two primality tests.

Author Biography

  • John H. Jaroma, Ave Maria University
    Assistant Professor of Mathematics

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Published

2009-08-18

Issue

Vol. 2 No. 3: (July 2009)

Section

Number Theory

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How to Cite

Equivalence of Pepin’s and the Lucas-Lehmer tests. (2009). European Journal of Pure and Applied Mathematics, 2(3), 352-360. https://www.ejpam.com/index.php/ejpam/article/view/245