A class of primality tests for trinomials which includes the Lucas-Lehmer test

Hugh C. Williams

Vol. 98 (1982), No. 2, 477–494

DOI: 10.2140/pjm.1982.98.477

Abstract

When n is an odd prime, the well-known Lucas-Lehmer test gives a necessary and sufficient condition for primality of 2ⁿ − 1. In this paper, primality tests of a similar character are developed for certain integers of the form Ab²ⁿ + Bbⁿ − 1 and a criterion which generalizes the Lucas-Lehmer test is obtained.

Mathematical Subject Classification

Primary: 10A25, 10A25

Milestones

Received: 6 March 1979

Revised: 6 March 1981

Published: 1 February 1982