On some new families of $k$-Mersenne and generalized $k$-Gaussian Mersenne numbers and their polynomials
DOI:
https://doi.org/10.55016/ojs/cdm.v18i2.74415Abstract
In this paper, we define the 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 their relation with the 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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Copyright (c) 2023 Munesh Kumari, Jagmohan Tanti, Kalika Prasad
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