On Some Recurrence Relations Connected with Generalized Fermat Numbers and Some Properties of Divisibility for these Numbers

Ahmet Ipek *

Department of Mathematics, Kamil O¨ zdag˘ Science Faculty, Karamanog˘ lu Mehmetbey University, Karaman, Turkey.

*Author to whom correspondence should be addressed.


Abstract

As a result of nice properties of Fermat numbers and their interesting applications, these numbers have recently seen a variety of developments and extensions. Within this framework, this paper contributes. The purpose of this paper is to obtain some recurrence relations connected with generalized Fermat numbers \(\mathcal{F}\)\(\mathcal{n}\) = \(\mathcal{a}\)2\(\mathcal{n}\) + 1 for \(\mathcal{a}\), \(\mathcal{n}\) \(\epsilon\) \(\mathbb{Z}\) and \(\mathcal{n}\) \(\geq\) 0 and as a result of these recurrent relations, to get some properties of divisibility for generalized Fermat numbers.

Keywords: Fermat number, recurrence relation, divisibility of integers


How to Cite

Ipek, A. (2024). On Some Recurrence Relations Connected with Generalized Fermat Numbers and Some Properties of Divisibility for these Numbers. Asian Journal of Advanced Research and Reports, 18(5), 38–42. https://doi.org/10.9734/ajarr/2024/v18i5630

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