In this paper, we extend Quadrapell numbers to Hyperbolic Quadarapell numbers, respectively. More... more In this paper, we extend Quadrapell numbers to Hyperbolic Quadarapell numbers, respectively. Moreover we obtain Binet-like formulas, generating functions and some identities related with Hyperbolic Quadarpell numbers.
In this study, we define hyperbolic-type k-Fibonacci numbers and then give the relationships betw... more In this study, we define hyperbolic-type k-Fibonacci numbers and then give the relationships between the k-step Fibonacci numbers and the hyperbolic-type k-Fibonacci numbers. In addition, we study the hyperbolic-type k-Fibonacci sequence modulo m and then we give periods of the Hperbolic-type k-Fibonacci sequences for any k and m which are related the periods of the k-step Fibonacci sequences modulo m. Furthermore, we extend the hyperbolic-type k-Fibonacci sequences to groups. Finally, we obtain the periods of the hyperbolic-type 2-Fibonacci sequences in the dihedral group D2m, (m ? 2) with respect to the generating pairs (x,y) and (y, x).
In this article, we extend Padovan and Pell-Padovan numbers to Hyperbolic Padovan and Hyperbolic ... more In this article, we extend Padovan and Pell-Padovan numbers to Hyperbolic Padovan and Hyperbolic Pell-Padovan numbers, respectively. Moreover, we obtain Binet-like formulas, generating functions and some identities related to Hyperbolic Padovan and Hyperbolic Pell-Padovan numbers.
Numerical Methods for Partial Differential Equations, 2020
The key agreement scheme is an important part of the cryptography theory. The first study in this... more The key agreement scheme is an important part of the cryptography theory. The first study in this field belongs to Diffie-Hellman and Merkle. We present a new key agreement scheme using a group action of special orthogonal group of 2 × 2 matrices with real entries on the complex projective line.
Let () 0 and () 0 be the Fibonacci and Padovan sequences given by the initial conditions 0 = 0, 1... more Let () 0 and () 0 be the Fibonacci and Padovan sequences given by the initial conditions 0 = 0, 1 = 1, 0 = 0, 1 = 2 = 1 and the recurrence formulas +2 = +1 + , +3 = +1 + for all , 0, respectively. In this note we study and completely solve the Diophantine * Supported by a CONACyT Doctoral Fellowship.
In this paper, we define the 2k-step Jordan-Fibonacci sequence, and then we study the 2k-step Jor... more In this paper, we define the 2k-step Jordan-Fibonacci sequence, and then we study the 2k-step Jordan-Fibonacci sequence modulo m. Also, we obtain the cyclic groups from the multiplicative orders of the generating matrix of the 2k-step Jordan-Fibonacci sequence when read modulo m, and we give the relationships among the orders of the cyclic groups obtained and the periods of the 2k-step Jordan-Fibonacci sequence modulo m. Furthermore, we extend the 2k-step Jordan-Fibonacci sequence to groups, and then we examine this sequence in the finite groups. Finally, we obtain the period of the 2k-step Jordan-Fibonacci sequence in the generalized quaternion group Q 2 n as applications of the results produced.
In this paper, we study the k-step α-generalized Pell-Padovan sequence modulo m. We define the k-... more In this paper, we study the k-step α-generalized Pell-Padovan sequence modulo m. We define the k-step α-generalized Pell-Padovan sequences in a finite group and we examine the periods of these sequences. Also, we obtain the periods of the k-step α-generalized Pell-Padovan sequences in the semidihedral group SD 2 m .
Fundamental Journal of Mathematics and Applications
In this study, we define the hyperbolic Jacobsthal-Lucas numbers and we obtain recurrence relatio... more In this study, we define the hyperbolic Jacobsthal-Lucas numbers and we obtain recurrence relations, Binet’s formula, generating function and the summation formulas for these numbers.
Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2019
In this manuscript, a new family of ݇ − Gaussian Fibonacci numbers has been identified and some r... more In this manuscript, a new family of ݇ − Gaussian Fibonacci numbers has been identified and some relationships between this family and known Gaussian Fibonacci numbers have been found. Also, I the generating functions of this family for ݇ = 2 has been obtained.
In this paper, we extend Quadrapell numbers to Hyperbolic Quadarapell numbers, respectively. More... more In this paper, we extend Quadrapell numbers to Hyperbolic Quadarapell numbers, respectively. Moreover we obtain Binet-like formulas, generating functions and some identities related with Hyperbolic Quadarpell numbers.
In this study, we define hyperbolic-type k-Fibonacci numbers and then give the relationships betw... more In this study, we define hyperbolic-type k-Fibonacci numbers and then give the relationships between the k-step Fibonacci numbers and the hyperbolic-type k-Fibonacci numbers. In addition, we study the hyperbolic-type k-Fibonacci sequence modulo m and then we give periods of the Hperbolic-type k-Fibonacci sequences for any k and m which are related the periods of the k-step Fibonacci sequences modulo m. Furthermore, we extend the hyperbolic-type k-Fibonacci sequences to groups. Finally, we obtain the periods of the hyperbolic-type 2-Fibonacci sequences in the dihedral group D2m, (m ? 2) with respect to the generating pairs (x,y) and (y, x).
In this article, we extend Padovan and Pell-Padovan numbers to Hyperbolic Padovan and Hyperbolic ... more In this article, we extend Padovan and Pell-Padovan numbers to Hyperbolic Padovan and Hyperbolic Pell-Padovan numbers, respectively. Moreover, we obtain Binet-like formulas, generating functions and some identities related to Hyperbolic Padovan and Hyperbolic Pell-Padovan numbers.
Numerical Methods for Partial Differential Equations, 2020
The key agreement scheme is an important part of the cryptography theory. The first study in this... more The key agreement scheme is an important part of the cryptography theory. The first study in this field belongs to Diffie-Hellman and Merkle. We present a new key agreement scheme using a group action of special orthogonal group of 2 × 2 matrices with real entries on the complex projective line.
Let () 0 and () 0 be the Fibonacci and Padovan sequences given by the initial conditions 0 = 0, 1... more Let () 0 and () 0 be the Fibonacci and Padovan sequences given by the initial conditions 0 = 0, 1 = 1, 0 = 0, 1 = 2 = 1 and the recurrence formulas +2 = +1 + , +3 = +1 + for all , 0, respectively. In this note we study and completely solve the Diophantine * Supported by a CONACyT Doctoral Fellowship.
In this paper, we define the 2k-step Jordan-Fibonacci sequence, and then we study the 2k-step Jor... more In this paper, we define the 2k-step Jordan-Fibonacci sequence, and then we study the 2k-step Jordan-Fibonacci sequence modulo m. Also, we obtain the cyclic groups from the multiplicative orders of the generating matrix of the 2k-step Jordan-Fibonacci sequence when read modulo m, and we give the relationships among the orders of the cyclic groups obtained and the periods of the 2k-step Jordan-Fibonacci sequence modulo m. Furthermore, we extend the 2k-step Jordan-Fibonacci sequence to groups, and then we examine this sequence in the finite groups. Finally, we obtain the period of the 2k-step Jordan-Fibonacci sequence in the generalized quaternion group Q 2 n as applications of the results produced.
In this paper, we study the k-step α-generalized Pell-Padovan sequence modulo m. We define the k-... more In this paper, we study the k-step α-generalized Pell-Padovan sequence modulo m. We define the k-step α-generalized Pell-Padovan sequences in a finite group and we examine the periods of these sequences. Also, we obtain the periods of the k-step α-generalized Pell-Padovan sequences in the semidihedral group SD 2 m .
Fundamental Journal of Mathematics and Applications
In this study, we define the hyperbolic Jacobsthal-Lucas numbers and we obtain recurrence relatio... more In this study, we define the hyperbolic Jacobsthal-Lucas numbers and we obtain recurrence relations, Binet’s formula, generating function and the summation formulas for these numbers.
Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2019
In this manuscript, a new family of ݇ − Gaussian Fibonacci numbers has been identified and some r... more In this manuscript, a new family of ݇ − Gaussian Fibonacci numbers has been identified and some relationships between this family and known Gaussian Fibonacci numbers have been found. Also, I the generating functions of this family for ݇ = 2 has been obtained.
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