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Repdigits as Product of Fibonacci and Pell numbers

Yıl 2021, Cilt: 6 Sayı: 1, 31 - 35, 30.04.2021

Öz

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.

Kaynakça

  • 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.
Yıl 2021, Cilt: 6 Sayı: 1, 31 - 35, 30.04.2021

Öz

Kaynakça

  • 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.
Toplam 9 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Volume VI Issue I 2021
Yazarlar

Abdullah Çağman 0000-0002-0376-7042

Yayımlanma Tarihi 30 Nisan 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 6 Sayı: 1

Kaynak Göster

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. Nisan 2021;6(1):31-35.
Chicago Çağman, Abdullah. “Repdigits As Product of Fibonacci and Pell Numbers”. Turkish Journal of Science 6, sy. 1 (Nisan 2021): 31-35.
EndNote Çağman A (01 Nisan 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, c. 6, sy. 1, ss. 31–35, 2021.
ISNAD Çağman, Abdullah. “Repdigits As Product of Fibonacci and Pell Numbers”. Turkish Journal of Science 6/1 (Nisan 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, c. 6, sy. 1, 2021, ss. 31-35.
Vancouver Çağman A. Repdigits as Product of Fibonacci and Pell numbers. TJOS. 2021;6(1):31-5.