Some new primality criteria based on Lucas sequences

Abstract

In this paper, we provide some novel results concerning the behavior of $\frac{U_{kn}}{U_k}$ modulo $U_n$, where $(U_n{)}_{n\in \mathbb{N}}$ is the Lucas sequence of the first kind. As a consequence, we obtain some primality criteria which do not seem to appear in the literature.

11 pages, comments welcome