Boonyen Thongkam and Nutcha Sailadda

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 24, 2018, Number 1, Pages 97—102

DOI: 10.7546/nntdm.2018.24.1.97-102

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## Details

### Authors and affiliations

Boonyen Thongkam

*Department of Mathematics, Faculty of Science
Ubon Ratchathani Rajabhat University
Ubon Ratchathani, 34000, Thailand*

Nutcha Sailadda

*Department of Mathematics, Faculty of Education
Ubon Ratchathani Rajabhat University
Ubon Ratchathani, 34000, Thailand
*

### Abstract

Abd-Elhameed and Zeyada have introduced the generalized sequence of numbers (*U _{n}^{a,b,r}*)

_{n≥0}such that sequence generalizes both generalized Fibonacci numbers (

*G*)

_{n}^{a,b}_{n≥0}and generalized Pell numbers (

*P*)

_{n}^{a,b}_{n≥0}. In the present paper, we show a study of the greatest common divisors of some

*G*,

_{n}^{a,b}*P*and

_{n}^{a,b}*U*.

_{n}^{a,b,r}### Keywords

- Greatest common divisor
- Generalized Fibonacci number
- Generalized Pell number

### 2010 Mathematics Subject Classification

- 11B39
- 11A05

### References

- Adb-Elhameed, W. M., & Zeyada, N. A. (2015) Some new identities of generalized Fibonacci and generalized Pell numbers via a new type of numbers, preprint, http://arxiv.org/abs/1511.07588v1.
- Chen, K. W. (2011) Greatest common divisors in shifted Fibonacci sequences. J. Integer Sequences, 14, 1–8 (Article 11.4.7). Available online at: https://cs.uwaterloo.ca/journals/JIS/VOL14/Chen/chen70.pdf.
- Dudley, U., & Tucker, B. (1971) Greatest common divisors in altered Fibonacci sequences, The Fibonacci Quarterly, 9, 89–91.
- Koshy, T. (2014) Pell and Pell–Lucas Numbers with Applications, Springer, Berlin.
- Koshy, T. (2001) Fibonacci and Lucas Numbers with Applications, Wiley–Interscience Publications.
- McDaniel, W. L. (1991) The G.C.D. in Lucas Sequences and Lehmer Number Sequences, The Fibonacci Quarterly, 29, 24–29.
- Raji, W. (2004) An introductory course in elementary number theory, Mobius.

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## Cite this paper

APAThongkam, B., & Sailadda, N. (2018). The greatest common divisors of generalized Fibonacci and generalized Pell numbers. Notes on Number Theory and Discrete Mathematics, 24(1), 97-102, doi: 10.7546/nntdm.2018.24.1.97-102.

ChicagoThongkam, Boonyen and Nutcha Sailadda. “The Greatest Common Divisors of Generalized Fibonacci and Generalized Pell Numbers.” Notes on Number Theory and Discrete Mathematics 24, no. 1 (2018): 97-102, doi: 10.7546/nntdm.2018.24.1.97-102.

MLAThongkam, Boonyen and Nutcha Sailadda. “The Greatest Common Divisors of Generalized Fibonacci and Generalized Pell Numbers.” Notes on Number Theory and Discrete Mathematics 24.1 (2018): 97-102. Print, doi: 10.7546/nntdm.2018.24.1.97-102.