Observations sur les triangles rectangles en nombres entiers et les suites de Fibonacci
On a binary recurrent sequence of polynomials
In this paper, we study the properties of the sequence of polynomials given by , for , where is non-constant and the characteristic of is . This complements some results from R. Euler, L.H. Gallardo: On explicit formulae and linear recurrent sequences, Acta Math. Univ. Comenianae, 80 (2011) 213-219.
On a constant of Turán and Erdös
On a Diophantine problem of Bennett
On a generalization of the Lucas functions
On a generalization of the Pell sequence
The Pell sequence is the second order linear recurrence defined by with initial conditions and . In this paper, we investigate a generalization of the Pell sequence called the -generalized Pell sequence which is generated by a recurrence relation of a higher order. We present recurrence relations, the generalized Binet formula and different arithmetic properties for the above family of sequences. Some interesting identities involving the Fibonacci and generalized Pell numbers are also deduced....
On a Problem of D'Atri and Nickerson.
On a Problem of W. Sierpinski.
On a product of sines
On an asymptotic formula for the Niven numbers.
On an extension of a theorem of S. Chowla
On Balancing and Lucas-balancing Quaternions
The aim of this article is to investigate two new classes of quaternions, namely, balancing and Lucas-balancing quaternions that are based on balancing and Lucas-balancing numbers, respectively. Further, some identities including Binet's formulas, summation formulas, Catalan's identity, etc. concerning these quaternions are also established.
On Bernoulli and Euler Numbers.
On certain ideals of the group ring
On generalized bihyperbolic Mersenne numbers
In this paper, a new generalization of Mersenne bihyperbolic numbers is introduced. Some of the properties of presented numbers are given. A general bilinear index-reduction formula for the generalized bihyperbolic Mersenne numbers is obtained. This result implies the Catalan, Cassini, Vajda, d'Ocagne and Halton identities. Moreover, generating function and matrix generators for these numbers are presented.
On generalized Fibonacci polynomials and Bernoulli numbers.
On Krasner's Criteria for the First Case of Fermat's Last Theorem.
On Legendre numbers.
On Legendre numbers of the second kind.
On linear differential equations involving a para-Grassmann variable.