On some new families of k-Mersenne and generalized k-Gaussian Mersenne numbers and their polynomials

2021/11/18 by Munesh Kumari, Kumari, Munesh, Jagmohan Tanti +3
Mathematics · Physics and Astronomy · #11B37 #11B39 #11B83 #Advanced Mathematical Identities #Advanced Mathematical Theories #Advanced Mathematical Theories and Applications #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #math.CO #math.NT #msc:11B37 #msc:11B39 #msc:11B83

paper · pdf · doi:10.48550/arxiv.2111.09592

16 pages

arxiv created 2021/11/18 · openalex publication_date 2021/11/18 · arxiv updated 2021/11/19 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

In this paper, we define new generalized k-Mersenne numbers and give a formula of generalized Mersenne polynomials and further we study their properties. Moreover, we define Gaussian Mersenne numbers and obtain some identities like Binet Formula, Cassini's identity, D'Ocagne's Identity, and generating functions. The generalized Gaussian Mersenne numbers are described and the relation with classical Mersenne numbers are explained. We also introduce a generalization of Gaussian Mersenne polynomials and establish some properties of these polynomials.

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