Gómez, Carlos A.Gómez, Jhonny C.Luca, Florian2025-07-082025-07-082024Gómez, C.A., Gómez, J.C. & Luca, F. A Diophantine Equation With Powers of Three Consecutive Fibonacci Numbers. Results Math 79, 136 (2024). https://doi.org/10.1007/s00025-024-02156-w14226383https://repositorio.usc.edu.co/handle/20.500.12421/7290The k–generalized Fibonacci sequence {Fn(k)}n≥2-k is the linear recurrent sequence of order k whose first k terms are 0,…,0,1 and each term afterwards is the sum of the preceding k terms. The case k=2 corresponds to the well known Fibonacci sequence {Fn}n≥0. In this paper we extend the study of the exponential Diophantine equation Fn+1x+Fnx-Fn-1x=Fm with terms Fr(k) instead of Fr, where r∈{n+1,n,n-1,m}.en11B3911D61 11J86exponential Diophantine equationFibonacci numberslower bounds for nonzero linear forms in logarithms of algebraic numbersArticle