Lucas numbers as sums of two repdigits

1. J.J. Bravo and F. Luca, On a conjecture about repdigits in k-generalized Fibonacci sequences, Publ. Math., 82(3–4): 623–639, 2013.

   MathSciNet  MATH  Google Scholar 

2. Y. Bugeaud, M. Maurice, and S. Siksek, Classical and modular approaches to exponential Diophantine equations I. Fibonacci and Lucas perfect powers, Ann. Math. (2), 163(3):969–1018, 2006.

   Article  MathSciNet  MATH  Google Scholar 

3. Y. Bugeaud and M. Mignotte, On integers with identical digits, Mathematika, 46(2):411–417, 1999.

   Article  MathSciNet  MATH  Google Scholar 

4. S. Díaz-Alvarado and F. Luca, Fibonacci numbers which are sums of two repdigits, in F. Luca and P. Stănică (Eds.), Proceedings of the 14th International Conference on Fibonacci Numbers and Their Applications, Morelia, Mexico, July 5–9, 2010, Aportaciones Mat., Investig., Vol. 20, Sociedad Matemática Mexicana, México, 2011, pp. 97–108.

5. A. Dujella and A. Pethő, A generalization of a theorem of Baker and Davenport, Q. J. Math., Oxf. II. Ser., 49(3):291–306, 1998.

   Article  MathSciNet  MATH  Google Scholar 

6. G.H. Hardy and E.M. Wright, An Introduction to the Theory of Numbers, 5th ed., Clarendon Press, Oxford, 1979.

   MATH  Google Scholar 

7. B. Kafle, F. Luca, and A. Togbé, x-coordinates of Pell equations which are Lucas numbers, Bol. Soc. Mat. Mex., III. Ser., to appear.

8. F. Luca, Distinct digits in base b expansions of linear recurrence sequences, Quaest. Math., 23(4):389–404, 2000.

   Article  MathSciNet  MATH  Google Scholar 

9. F. Luca, Fibonacci and lucas numbers with only one distinct digit, Port. Math., 57(2):243–254, 2000.

   MathSciNet  MATH  Google Scholar 

10. F. Luca, Repdigits which are sums of at most three Fibonacci number, Math. Commun., 17(1):1–11, 2012.

    Google Scholar 

11. D. Marques and A. Togbé, On terms of linear recurrence sequences with only one distinct block of digits, Colloq. Math., 124:145–155, 2011.

    Article  MathSciNet  MATH  Google Scholar 

12. D. Marques and A. Togbé, On repdigits as product of consecutive Fibonacci numbers, Rend. Ist. Mat. Univ. Trieste, 44(1):393–397, 2012.

    MathSciNet  MATH  Google Scholar 

13. E.M. Matveev, An explicit lower bound for a homogeneous rational linear form in logarithms of algebraic numbers. II, Izv. Ross. Akad. Nauk, Ser. Mat., 64:125–180, 2000. English transl.: Izv. Math., 64:1217–1269, 2000

14. R. Obláth, Une propriété des puissances parfaites, Mathesis, 65:356–364, 1956.

    MathSciNet  MATH  Google Scholar 

15. C.L. Stewart, On the representation of an integer in two different bases, J. Reine Angew. Math., 319:63–72, 1980.

    MathSciNet  MATH  Google Scholar 

Download references