The greatest common divisors of generalized Fibonacci and generalized Pell numbers

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
Full paper (PDF, 141 Kb)

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_n^a,b and U_n^a,b,r.

Keywords

• Greatest common divisor
• Generalized Fibonacci number
• Generalized Pell number

2010 Mathematics Subject Classification

• 11B39
• 11A05

References

1. 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.
2. 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.
3. Dudley, U., & Tucker, B. (1971) Greatest common divisors in altered Fibonacci sequences, The Fibonacci Quarterly, 9, 89–91.
4. Koshy, T. (2014) Pell and Pell–Lucas Numbers with Applications, Springer, Berlin.
5. Koshy, T. (2001) Fibonacci and Lucas Numbers with Applications, Wiley–Interscience Publications.
6. McDaniel, W. L. (1991) The G.C.D. in Lucas Sequences and Lehmer Number Sequences, The Fibonacci Quarterly, 29, 24–29.
7. Raji, W. (2004) An introductory course in elementary number theory, Mobius.