On Some Recurrence Relations Connected with Generalized Fermat Numbers and Some Properties of Divisibility for these Numbers
Asian Journal of Advanced Research and Reports · pp. 38–42 · Published 18 Mar 2024
10.9734/ajarr/2024/v18i5630Abstract
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.
References (6)
- 1 The Higher Arithmetic : An Introduction to the Theory of Numbers
- 2 Elementary Number Theory with Applications
- 3 Mersenne Numbers and Fermat Numbers [DOI]
- 4 Mersenne and Fermat Numbers [DOI]
- 5 A note on factors of generalized Fermat numbers [DOI]
- 6 The On-Line Encyclopedia of Integer Sequences [DOI]
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