Fibonacci Sums Modulo 5

[1] K. Adegoke, Weighted sums of some second-order sequences, Fibonacci Quart. 56 (2018), no. 3, 252–262. Search in Google Scholar

[2] K. Adegoke, R. Frontczak, and T. Goy, New binomial Fibonacci sums, Palest. J. Math. 13 (2024), no. 1, 323–339. Search in Google Scholar

[3] K. Adegoke, R. Frontczak, and T. Goy, Binomial Fibonacci sums from Chebyshev polynomials, J. Integer Seq. 26 (2023), no. 9, Paper No. 23.9.6, 26 pp. Search in Google Scholar

[4] K. Adegoke, R. Frontczak, and T. Goy, On Fibonacci and Lucas binomial sums modulo 5, in: XIX International Scientific Mykhailo Kravchuk Conference. Abstracts, I. Sikorsky Kyiv Polytechnic Institute, Kyiv, 2023, pp. 60–61. Search in Google Scholar

[5] K. Adegoke, A. Olatinwo, and S. Ghosh, Cubic binomial Fibonacci sums, Electron. J. Math. 2 (2021), 44–51. Search in Google Scholar

[6] M. Bai, W. Chu, and D. Guo, Reciprocal formulae among Pell and Lucas polynomials, Mathematics 10 (2022), no. 15, 2691, 11 pp. Search in Google Scholar

[7] Z. Fan and W. Chu, Convolutions involving Chebyshev polynomials, Electron. J. Math. 3 (2022), 38–46. Search in Google Scholar

[8] R. Frontczak and T. Goy, Chebyshev-Fibonacci polynomial relations using generating functions, Integers 21 (2021), Paper No. A100, 15 pp. Search in Google Scholar

[9] I. Gradshteyn and I. Ryzhik, Table of Integrals, Series, and Products, Elsevier/Academic Press, Amsterdam, 2015. Search in Google Scholar

[10] E. Hansen, Addendum for ‘A Table of Series and Products’, preprint (undated), 56 pp. Available at carmamaths.org/resources/jon/Preprints/Books/Other/hansen07.pdf. Search in Google Scholar

[11] E. Kılıç, S. Koparal, and N. Ömür, Powers sums of the first and second kinds of Chebyshev polynomials, Iran. J. Sci. Technol. Trans. A Sci. 44 (2020), no. 2, 425–435. Search in Google Scholar

[12] T. Koshy, Fibonacci and Lucas Numbers with Applications, Wiley-Interscience, New York, 2001. Search in Google Scholar

[13] D.J. Leeming, The coefficients of sinh xt= sin t and the Bernoulli polynomials, Internat. J. Math. Ed. Sci. Tech. 28 (1997), no. 4, 575–579. Search in Google Scholar

[14] C. Li and Z. Wenpeng, Chebyshev polynomials and their some interesting applications, Adv. Difference Equ. (2017), Paper No. 303, 9 pp. Search in Google Scholar

[15] Y. Li, On Chebyshev polynomials, Fibonacci polynomials, and their derivatives, J. Appl. Math. (2014), Art. ID 451953, 8 pp. Search in Google Scholar

[16] J.C. Mason and D.C. Handscomb, Chebyshev Polynomials, Chapman & Hall/CRC, Boca Raton, FL, 2003. Search in Google Scholar

[17] N.J.A. Sloane (ed.), The On-Line Encyclopedia of Integer Sequences. Available at oeis.org/book.html. Search in Google Scholar

[18] S. Vajda, Fibonacci and Lucas Numbers, and the Golden Section. Theory and Applications, Dover Publications, Inc., Mineola, NY, 2008. Search in Google Scholar

[19] W. Zhang, On Chebyshev polynomials and Fibonacci numbers, Fibonacci Quart. 40 (2002), no. 5, 424–428. Search in Google Scholar