Abstract
In this paper, we find all the Padovan and Perrin numbers which are product of two repdigits.
Similar content being viewed by others
References
Baker, A., Davenport, H.: The equations \(3x^2 - 2 = y^2\) and \(8x^2 - 7 = z^2\). Quart. J. Math. Oxford Ser. 20, 129–137 (1969)
Bugeaud, Y., Maurice, M., Siksek, S.: Classical and modular approaches to exponential Diophantine equations I. Fibonacci and Lucas perfect powers. Ann. Math. 163, 969–1018 (2006)
Erduvan, F., Keskin, R.: Fibonacci and Lucas numbers as products of two repdigits. Turk. J. Math. 43, 2142–2153 (2019)
Dujella, A., Pethő, A.: A generalization of a theorem of Baker and Davenport. Quart. J. Math. Oxford Ser. 49(195), 291–306 (1998)
Lomelí, A. C. G., Hernández, S. H.: Repdigits as sums of two Padovan numbers. J. Integer Sequences, 22 (2019), Article 19.2.3
Matveev, E.M.: An explicit lower bound for a homogeneous rational linear form in the logarithms of algebraic numbers, II. Izv. Math. 64(6), 1217–1269 (2000)
de Weger, B. M. M.: Algorithms for Diophantine equations, Stichting Mathematisch Centrum, (1989)
Acknowledgements
The authors are grateful to the referee for the useful comments that help to improve the quality of this paper.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Rihane, S.E., Togbé, A. Padovan and Perrin numbers as product of two repdigits. Bol. Soc. Mat. Mex. 28, 51 (2022). https://doi.org/10.1007/s40590-022-00446-3
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s40590-022-00446-3