On the k-Mersenne–Lucas numbers
Mourad Chelgham,Ali Boussayoud +1 more
- Vol. 27, Iss: 1, pp 7-13
TLDR
In this article, a new definition of k-Mersenne-Lucas numbers was introduced and properties of these numbers were investigated, and some identities and established connection formulas between them through the use of Binet's formula.Abstract:
In this paper, we will introduce a new definition of k-Mersenne–Lucas numbers and investigate some properties. Then, we obtain some identities and established connection formulas between k-Mersenne–Lucas numbers and k-Mersenne numbers through the use of Binet’s formula.read more
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On the bivariate Mersenne Lucas polynomials and their properties
Nabiha Saba,Ali Boussayoud +1 more
TL;DR: In this article, a new concept of bivariate Mersenne Lucas polynomials is introduced and the recurrence relation of them is given, and Binet's formula, generating function, Catalan's identity and Cassini's identity for this type of polynomial are obtained.
Journal ArticleDOI
On the Mersenne and Mersenne-Lucas hybrinomial quaternions
TL;DR: In this article , the Mersenne hybrinomial quaternions were introduced and some properties of these polynomials were derived, such as Binet formulas, Catalan, Cassini, d'Ocagne identity and generating and exponential generating function.
On $k$-Mersenne and k-Mersenne-Lucas Octonions
TL;DR: The closed form formulae for these octonions are given and some well-known identities like Cassini's identity, d’Ocagne’s identity, Catalan identity, Vajda's identity and generating functions of them are obtained.
The sequence of higher order Mersenne numbers and associated binomial transforms
TL;DR: In this article , a higher order Mersenne sequence is introduced and studied, which is analogous to the higher order Fibonacci numbers and closely associated with the Mersenzenne numbers.
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