TY - JOUR
AU - Altassan, Alaa
AU - Alan, Murat
PY - 2024/01/29
Y2 - 2024/06/17
TI - Mersenne Numbers in Generalized Lucas Sequences
JF - Proceedings of the Bulgarian Academy of Sciences
JA - C. R. Acad. Bulg. Sci.
VL - 77
IS - 1
SE - Mathematics
DO - 10.7546/CRABS.2024.01.01
UR - https://proceedings.bas.bg/index.php/cr/article/view/453
SP - 3-10
AB - <p>Let $$k \geq 2$$ be an integer and let $$(L_{n}^{(k)})_{n \geq 2-k}$$ 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.</p>
ER -