### Primality test with pair of Lucas sequences

#### Abstract

Lucas sequences and their applications play vital role in the study of primality tests in number theory. There are several known tests for primality of positive integer $N$ using Lucas sequences which are based on factorization of $(N \pm 1)$ [2] [13]. In this paper we give a primality test for odd positive integer $N>1$ by using the set $L(\Delta, N)$ where $L(\Delta, N)$ is a set of $S(N)$ distinct pair of Lucas sequences $(V_n (a,1),U_n (a,1))$, where $S(N)$ for $N=p_1^{e_1}.p_2^{e_2}\ldots p_s^{e_s}$ is given as $S(N)=LCM[\{p_{i}^{e_{i}-1}(p_i-(\frac{\Delta}{p_i}))\}_{i=1}^s]$ and $\Delta=a^2-4$ for some fixed integer $a$.

**Published:**2020-09-29

**How to Cite this Article:**P. Anuradha Kameswari, B. Ravitheja, Primality test with pair of Lucas sequences, J. Math. Comput. Sci., 10 (2020), 2544-2556 Copyright © 2020 P. Anuradha Kameswari, B. Ravitheja. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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