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Original Articles

On The diophantine equation Fn+Fm=2a

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Pages 391-400 | Received 11 Mar 2014, Published online: 07 Dec 2015

References

  • A. Baker and H. Davenport, The equations 3x2−2 = y2 and 8x2−7 = z2, Quart.J. Math. Oxford Ser. (2) 20(1) (1969), 129–137.
  • Yu. Bilu, G. Hanrot and P. Voutier, Existence of primitive divisors of Lucas and Lehmer numbers (with an appendix by M. Mignotte), J. Reine Angew. Math. 539 (2001), 75–122.
  • J.J. Bravo and F. Luca, On a conjecture about repdigits in k−generalized Fi- bonacci sequences, Publ. Math. Debrecen 82(3–4) (2013), 623–639.
  • Y. Bugeaud, M. Mignotte and S. Siksek, Classical and modular approaches to exponential Diophantine equations. I. Fibonacci and Lucas perfect powers, Ann. of Math. (2) 163(3) (2006), 969–1018.
  • R.D. Carmichael, On the numerical factors of the arithmetic forms αn ± βn, Ann. Math. 15(1/4) (1913), 30–70.
  • S. D´ıaz Alvarado and F. Luca, Fibonacci numbers which are sums of two repdigits, Proceedings of the XIVth International Conference on Fibonacci numbers and their applications (Editors: F. Luca and P. Stanica), pp. 97–111, 2011.
  • A. Dujella and A. Petho˝, A generalization of a theorem of Baker and Davenport, Quart. J. Math. Oxford Ser. (2) 49(3) (1998), 291–306.
  • T. Koshy, Fibonacci and Lucas Numbers with Applications, Wiley-Interscience Pub- lication, New York, 2001.
  • F. Luca, Repdigits as sums of three Fibonacci numbers, Math. Commun. 17 (2012), 1–11.
  • F. Luca and S. Siksek, On factorials expressible as sums of at most three Fibonacci numbers, Proc. Edinb. Math. Soc. (2) 53(3) (2010), 747–763.
  • E.M. Matveev, An explicit lower bound for a homogeneous rational linear form in the logarithms of algebraic numbers. II, Izv. Ross. Akad. Nauk Ser. Mat. 64(6) (2000), 125–180 (Russian). Translation in Izv. Math. 64(6) (2000), 1217–1269.
  • A. Petho˝ and R.F. Tichy, S-unit equations, linear recurrences and digit expansions, Publ. Math. Debrecen 42(1–2) (1993), 145–154.
  • H.G. Senge and E.G. Straus, PV-numbers and sets of multiplicity, Period. Math. Hungar. 3 (1973), 93–100.
  • C.L. Stewart, On the representation of an integer in two different bases, J. Reine Angew. Math. 319 (1980), 63–72.
  • E. Zeckendorf, Repr´esentation des nombres naturels par une somme de nombres de Fibonacci ou de nombres de Lucas, Bull. Soc. Roy. Sci. Li`ege 41 (1972), 179–182 ( French).

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