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Repdigits as Product of Fibonacci and Pell numbers

Year 2021, Volume: 6 Issue: 1, 31 - 35, 30.04.2021

Abstract

In this paper, we find all repdigits which can be expressed as the product of a Fibonacci number and a Pell number. We use of a combined approach of lower bounds for linear forms in logarithms of algebraic numbers and a version of the Baker-Davenport reduction method to prove our main result.

References

  • Jhon J Bravo and Florian Luca. On a conjecture about repdigits in k-generalized fibonacci sequences. Publ. Math. Debrecen, 82(3-4):623–639, 2013.
  • Yann Bugeaud, Maurice Mignotte, and Samir Siksek. Classical and modular approaches to exponential diophantine equations i. fibonacci and lucas perfect powers. Annals of Mathematics, pages 969–1018, 2006.
  • Mahadi Ddamulira. Repdigits as sums of three padovan numbers. Bolet´ın de la Sociedad Matem´atica Mexicana, pages 1–15, 2019.
  • Andrej Dujella and Attila Petho. A generalization of a theorem of baker and davenport. The Quarterly Journal of Mathematics, 49(195):291–306, 1998.
  • Fatih Erduvan, Refik Keskin, and Zafer S¸iar. Repdigits base b as products of two lucas numbers. Quaestiones Mathematicae, pages 1–11, 2020.
  • Florian Luca. Repdigits as sums of three fibonacci numbers. Mathematical Communications, 17(1):1–11, 2012.
  • Eugene M Matveev. An explicit lower bound for a homogeneous rational linear form in the logarithms of algebraic numbers. ii. Izvestiya: Mathematics, 64(6):1217, 2000.
  • Zafer Siar, Fatih Erduvan, and Refik Keskin. Repdigits as products of two pell or pell-lucas numbers. Acta Mathematica Universitatis Comenianae, 88(2):247–256, 2019.
  • Nigel P Smart. The algorithmic resolution of Diophantine equations: a computational cookbook, volume 41. Cambridge University Press, 1998.
Year 2021, Volume: 6 Issue: 1, 31 - 35, 30.04.2021

Abstract

References

  • Jhon J Bravo and Florian Luca. On a conjecture about repdigits in k-generalized fibonacci sequences. Publ. Math. Debrecen, 82(3-4):623–639, 2013.
  • Yann Bugeaud, Maurice Mignotte, and Samir Siksek. Classical and modular approaches to exponential diophantine equations i. fibonacci and lucas perfect powers. Annals of Mathematics, pages 969–1018, 2006.
  • Mahadi Ddamulira. Repdigits as sums of three padovan numbers. Bolet´ın de la Sociedad Matem´atica Mexicana, pages 1–15, 2019.
  • Andrej Dujella and Attila Petho. A generalization of a theorem of baker and davenport. The Quarterly Journal of Mathematics, 49(195):291–306, 1998.
  • Fatih Erduvan, Refik Keskin, and Zafer S¸iar. Repdigits base b as products of two lucas numbers. Quaestiones Mathematicae, pages 1–11, 2020.
  • Florian Luca. Repdigits as sums of three fibonacci numbers. Mathematical Communications, 17(1):1–11, 2012.
  • Eugene M Matveev. An explicit lower bound for a homogeneous rational linear form in the logarithms of algebraic numbers. ii. Izvestiya: Mathematics, 64(6):1217, 2000.
  • Zafer Siar, Fatih Erduvan, and Refik Keskin. Repdigits as products of two pell or pell-lucas numbers. Acta Mathematica Universitatis Comenianae, 88(2):247–256, 2019.
  • Nigel P Smart. The algorithmic resolution of Diophantine equations: a computational cookbook, volume 41. Cambridge University Press, 1998.
There are 9 citations in total.

Details

Primary Language English
Journal Section Volume VI Issue I 2021
Authors

Abdullah Çağman 0000-0002-0376-7042

Publication Date April 30, 2021
Published in Issue Year 2021 Volume: 6 Issue: 1

Cite

APA Çağman, A. (2021). Repdigits as Product of Fibonacci and Pell numbers. Turkish Journal of Science, 6(1), 31-35.
AMA Çağman A. Repdigits as Product of Fibonacci and Pell numbers. TJOS. April 2021;6(1):31-35.
Chicago Çağman, Abdullah. “Repdigits As Product of Fibonacci and Pell Numbers”. Turkish Journal of Science 6, no. 1 (April 2021): 31-35.
EndNote Çağman A (April 1, 2021) Repdigits as Product of Fibonacci and Pell numbers. Turkish Journal of Science 6 1 31–35.
IEEE A. Çağman, “Repdigits as Product of Fibonacci and Pell numbers”, TJOS, vol. 6, no. 1, pp. 31–35, 2021.
ISNAD Çağman, Abdullah. “Repdigits As Product of Fibonacci and Pell Numbers”. Turkish Journal of Science 6/1 (April 2021), 31-35.
JAMA Çağman A. Repdigits as Product of Fibonacci and Pell numbers. TJOS. 2021;6:31–35.
MLA Çağman, Abdullah. “Repdigits As Product of Fibonacci and Pell Numbers”. Turkish Journal of Science, vol. 6, no. 1, 2021, pp. 31-35.
Vancouver Çağman A. Repdigits as Product of Fibonacci and Pell numbers. TJOS. 2021;6(1):31-5.