Equivalence of Pepin's and the Lucas-Lehmer tests
Year: 2009
Type: article
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: John H. Jaroma
Institution: Ave Maria University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W2189031828