| Issue |
EPJ Web Conf.
Volume 369, 2026
4th International Conference on Artificial Intelligence and Applied Mathematics (JIAMA’26)
|
|
|---|---|---|
| Article Number | 02013 | |
| Number of page(s) | 12 | |
| Section | XAI and Data-Driven Optimization in Energy, Environment, and Economic Systems | |
| DOI | https://doi.org/10.1051/epjconf/202636902013 | |
| Published online | 13 May 2026 | |
https://doi.org/10.1051/epjconf/202636902013
Mersenne Primes in Certain Lucas Sequences
1 Faculty of Computer Science and Mathematics, University of Kufa, Iraq
2 Faculty of Computer Science and Mathematics, University of Kufa, Iraq
* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
Published online: 13 May 2026
Abstract
Prime numbers are the most important numbers in number theory and cryptography. One of such special primes are given by the set of Mersenne primes, that are derived from the form Mn = 2n − 1, where n is a prime number. In this paper, we examine the appearance of these primes in certain sequences of Lucas numbers of the first kind {Un(P,Q)} or the second kind {Vn(P,Q)}. Namely, we completely solve the Diophantine equation Mn = Un(P,Q) or Mn = Vn(P,Q) for certain nonzero relatively prime parameters P and Q.
Key words: Prime numbers / Mersenne prime number / Lucas sequences / Diophantine equation / Elliptic curve
© The Authors, published by EDP Sciences, 2026
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