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