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Padovan and Perrin numbers as product of two repdigits

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Abstract

In this paper, we find all the Padovan and Perrin numbers which are product of two repdigits.

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References

  1. 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)

    Article  MathSciNet  Google Scholar 

  2. 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)

    Article  MathSciNet  Google Scholar 

  3. Erduvan, F., Keskin, R.: Fibonacci and Lucas numbers as products of two repdigits. Turk. J. Math. 43, 2142–2153 (2019)

    Article  MathSciNet  Google Scholar 

  4. Dujella, A., Pethő, A.: A generalization of a theorem of Baker and Davenport. Quart. J. Math. Oxford Ser. 49(195), 291–306 (1998)

    Article  MathSciNet  Google Scholar 

  5. Lomelí, A. C. G., Hernández, S. H.: Repdigits as sums of two Padovan numbers. J. Integer Sequences, 22 (2019), Article 19.2.3

  6. 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)

    Article  MathSciNet  Google Scholar 

  7. de Weger, B. M. M.: Algorithms for Diophantine equations, Stichting Mathematisch Centrum, (1989)

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Acknowledgements

The authors are grateful to the referee for the useful comments that help to improve the quality of this paper.

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Correspondence to Salah Eddine Rihane.

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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

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  • DOI: https://doi.org/10.1007/s40590-022-00446-3

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