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A Diophantine Equation With Powers of Three Consecutive k-Fibonacci Numbers
(Birkhauser, 2024) Gómez, Carlos A.; Gómez, Jhonny C.; Luca, Florian
The 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}.