The class of Lucas-Lehmer polynomials

Abstract

In this paper we introduce a new sequence of polynomials, which follow the same recursive rule of the well-known Lucas-Lehmer integer sequence. We show the most important properties of this sequence, relating them to the Chebyshev polynomials of the first and second kind.

Keywords

• chebyshev polynomials
• lucas-lehmer primality test
• lucas-lehmer primality numbers
• orthogonal polynomials
• zeros of polynomials