Repdigits as Euler functions of Lucas numbers

[1] A. Baker and H. Davenport,“The equations 3x2 - 2 = y2 and 8x2 - 7 = z2”, Quart. J. Math. Oxford Ser. (2) 20 (1969), 129-137.10.1093/qmath/20.1.129Search in Google Scholar

[2] J. J. Bravo and F. Luca,“On a conjecture about repdigits in k- generalized Fibonacci sequences”, Publ. Math. Debrecen, 82 (2013), 623-639.10.5486/PMD.2013.5390Open DOISearch in Google Scholar

[3] Y. Bugeaud, M. Mignotte and S. Siksek,“Classical and modular ap- proaches to exponential Diophantine equations. I. Fibonacci and Lucas perfect powers”, Ann. of Math. (2) 163 (2006), 969-1018.10.4007/annals.2006.163.969Search in Google Scholar

[4] Y. Bugeaud, F. Luca, M. Mignotte and S. Siksek,“Almost powers in the Lucas sequence”, J. N. T. Bordeaux 20 (2008), 555-600.10.5802/jtnb.642Search in Google Scholar

[5] R. D. Carmichael,“On the numerical factors of the arithmetic forms _n _ _n”, Ann. Math. (2) 15 (1913), 30-70.10.2307/1967797Open DOISearch in Google Scholar

[6] M. T. Damir, B. Faye, F. Luca and A. Tall,“Members of Lucas sequences whose Euler function is a power of 2”, Fibonacci Quarterly, to appear.Search in Google Scholar

[7] A. Dujella and A. Peth}o,“A generalization of a theorem of Baker and Davenport”, Quart. J. Math. Oxford Ser. (2) 49 (1998), 291-306.10.1093/qmathj/49.3.291Search in Google Scholar

[8] F. Luca,“Equations involving arithmetic functions of Fibonacci num- bers,” Fibonacci Quart. 38 (2000), 49-55.Search in Google Scholar

[9] F. Luca,“Euler indicators of binary recurrent sequences”, Collectanea Math. 53 (2002), 133-156.Search in Google Scholar

[10] F. Luca and M. Mignotte,“_(F11) = 88”, Divulgaciones Mat. 14 (2006), 101-106.Search in Google Scholar

[11] E. M. Matveev,“An explicit lower bound for a homogeneous rational linear form in the logarithms of algebraic numbers”, Izv. Math. 64 (2000), 1217-1269.10.1070/IM2000v064n06ABEH000314Search in Google Scholar

[12] W. L. McDaniel and P. Ribenboim,“Square-classes in Lucas sequences having odd parameters”, J. Number Theory 73 (1998), 14-27.10.1006/jnth.1998.2280Search in Google Scholar