Fibonacci numbers as mixed concatenations of Fibonacci and Lucas numbers

References

[1] Alan, M.: On concatenations of Fibonacci and Lucas numbers, Bull. Iran. Math. Soc. 48 (2022), 2725–2741.10.1007/s41980-021-00668-7Search in Google Scholar

[2] Alahmadi, A.—Altassan, A.—Luca, F.—Shoaib, H.: Fibonacci numbers which are concatenations of two repdigits, Quaest. Math. 44 (2021), 281–290.10.2989/16073606.2019.1686439Search in Google Scholar

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

[4] Banks, W. D.—Luca, F.: Concatenations with binary reccurent sequences, J. Integer Seq. 8 (2005), Art. 05.1.3.Search in Google Scholar

[5] Bravo, J. J.—Gómez, C. A.—Luca, F.: Powers of two as sums of two k-Fibonacci numbers, Miskolc Math. Notes 17(1) (2016), 85–100.10.18514/MMN.2016.1505Search in Google Scholar

[6] Bravo, E. F.—Bravo, J. J.: Tribonacci numbers with two blocks of repdigits, Math. Slovaca 71 (2021), 267–274.10.1515/ms-2017-0466Search in Google Scholar

[7] Bugeaud, Y.—Mignotte, M.—Siksek, S.: Classical and modular approaches to exponential Diophantine equations I. Fibonacci and Lucas perfect powers, Ann. of Math. 163 (2006), 969–1018.10.4007/annals.2006.163.969Search in Google Scholar

[8] Ddamulira, M.: Padovan numbers that are concatenations of two distinct repdigits, Math. Slovaca 71 (2021), 275–284.10.1515/ms-2017-0467Search in Google Scholar

[9] Dujella, A.—Pethő, A.: A generalization of a theorem of Baker and Davenport, Quart. J. Math. Oxford Ser. 49 (1998), 291–306.10.1093/qjmath/49.195.291Search in Google Scholar

[10] Erduvan, F.—Keskin, R.: Lucas numbers which are concatenations of three repdigits, Results Math. 76 (2021), Art. No. 13.10.1007/s00025-020-01314-0Search in Google Scholar

[11] Falcón, S.—Plaza, Á.: On the Fibonacci k-numbers, Chaos Solitons Fractals 32(5) (2007), 1615–1624.10.1016/j.chaos.2006.09.022Search in Google Scholar

[12] Hensley, D.: Continued Fractions, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2006.10.1142/9789812774682Search in Google Scholar

[13] Kaddoura, I.—Mourad, B.: On a new improved unifying closed formula for all Fibonacci-type sequences and some applications, J. Number Theory 182 (2018), 271–283.10.1016/j.jnt.2017.06.014Search in Google Scholar

[14] Koshy, T.: Fibonacci and Lucas Numbers with Applications, Wiley-Interscience Publications, 2001.10.1002/9781118033067Search in Google Scholar

[15] Kramer, J.—Hoggatt, Jr. V. E.: Special cases of Fibonacci periodicity, Fibonacci Quart. 10 (1972), 519–522.10.1080/00150517.1972.12430898Search in Google Scholar

[16] Laugier, A.—Saikia, M. P.: Some properties of Fibonacci numbers, generalized Fibonacci numbers and generalized Fibonacci polynomial sequences, Kyungpook Math. J. 57 (2017), 1–84.10.5666/KMJ.2017.57.1.1Search in Google Scholar

[17] Matveev, E. M.: An explicit lower bound for a homogeneous rational linear form in the logarithms of algebraic numbers II, Izv. Ross. Akad. Nauk Ser. Mat. 64 (2000), 125–180; translation in Izv. Math. 64 (2000), 1217–1269.Search in Google Scholar

[18] Özkan, E.—Altun, İ.—GÖçER, A.: On relationship among a new family of k-Fibonacci, k-Lucas numbers, Fibonacci and Lucas numbers, Chiang Mai J. Sci. 44(3) (2017), 1744–1750.Search in Google Scholar

[19] Özkan, E.—Aydoğdu, A.—Altun, İ.: Some identities for a family of Fibonacci and Lucas numbers, J. Math. Stat. Sci. 3(10) (2017), 295–303.Search in Google Scholar

[20] Qu, Y.—Zeng, J.: Lucas numbers which are concatenations of two repdigits, Mathematics 8(8) (2020), Art. No. 1360.10.3390/math8081360Search in Google Scholar

[21] Stanimirović, P.—Nikolov, J.—Stanimirović, I.: A generalization of Fibonacci and Lucas matrices, Discrete Appl. Math. 156(14) (2008), 2606–2619.10.1016/j.dam.2007.09.028Search in Google Scholar

[22] Trojovsky, P.: On Fibonacci numbers with a prescribed block of digits, Mathematics 8(4) (2020), Art. No. 639.10.3390/math8040639Search in Google Scholar

[23] Yilmaz, N.—Aydoğdu, A.—Özkan, E.: Some properties of k-Generalized Fibonacci numbers, Math. Montisnigri 50 (2021), 73–79.10.20948/mathmontis-2021-50-7Search in Google Scholar