MERSENNE NUMBERS IN GENERALIZED LUCAS SEQUENCES

Abstract

Let k >= 2 be an integer and let (L-n((k)))(n >= 2-k) be the k-generalized Lucas sequence with certain initial k terms and each term afterward is the sum of the k preceding terms. Mersenne numbers are the numbers of the form 2(a)-1, where a is any positive integer. The aim of this paper is to determine all Mersenne numbers which lie inside k-Lucas sequences.