A positive integer is called a repdigit if it has only one distinct digit in its decimal expansion. In this paper, we find all repdigits that are products of consecutive Pell or Pell–Lucas numbers. This paper continues previous work which dealt with finding occurrences of repdigits in the Pell and Pell–Lucas sequences.

Type of Study: Research paper |
Subject:
General

1. A. Baker, H. Davenport, The Equations 3x2 − 2 = y2 and 8x2 − 7 = z2, Quart. J. Math. Oxford Ser., 20, (1969), 129-137. [DOI:10.1093/qmath/20.1.129]

2. E. F. Bravo, C. A. G'omez, F. Luca, Product of consecutive Tribonacci Numbers with only One Distinct Digit, J. Integer Seq., 22, (2019), Article 19.6.3.

3. J. J. Bravo, C. A. G'omez, F. Luca, Powers of Two as Sums of Two k-Fibonacci Numbers, Miskolc Math. Notes, 17, (2016), 85-100. [DOI:10.18514/MMN.2016.1505]

4. J. J. Bravo, F. Luca, On a Conjecture about Repdigits in k-generalized Fibonacci Sequences, Publ. Math. Debrecen, 82, (2013), 623-639. [DOI:10.5486/PMD.2013.5390]

5. A. Dujella, A. Peth˝o, A Generalization of a Theorem of Baker and Davenport, Quart. J. Math. Oxford Ser., 49, (1998), 291-306. [DOI:10.1093/qjmath/49.195.291]

6. F. Erduvan, R. Keskin, Z. S¸iar, Repdigits as Product of Two Pell or Pell-Lucas Numbers, Acta Math. Univ. Comenianae, 88, (2019), 247-256.

7. B. Faye, F. Luca, Pell and Pell-Lucas Numbers with only One Distinct Digit, Ann. Math. Inform., 45, (2015), 55-60.

8. N. Irmak, A. Togb'e, On Repdigits as Product of Consecutive Lucas Numbers, Notes on Number Theory and Discrete Math., 24, (2018), 95-102. [DOI:10.7546/nntdm.2018.24.3.95-102]

9. F. Luca, Fibonacci and Lucas Numbers with only One Distinct Digit, Port. Math., 57, (2000), 243-254.

10. D. Marques, On k-generalized Fibonacci Numbers with only One Distinct Digit, Util. Math., 98, (2015), 23-31.

11. D. Marques, A. Togb'e, On Repdigits as Product of Consecutive Fibonacci Numbers, Rend. Istit. Mat. Univ. Trieste, 44, (2012), 393-397.

12. E. M. Matveev, An Explicit Lower Bound for a Homogeneous Rational Linear Form in the Logarithms of Algebraic Numbers, English translation in Izv. Math., 64, (2000), [DOI:10.1070/IM2000v064n06ABEH000314]

13. C. Sanna, The p-adic Valuation of Lucas Sequences, Fibonacci Quart., 54, (2016), 118-124.

14. N. J. Sloane, The On-Line Encyclopedia of Integer Sequences, http://oeis.org.

Rights and permissions | |

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. |