On Terms of Generalized Fibonacci Sequences which are Powers of their Indexes Article Swipe

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Pavel Trojovský ·

YOU? · · 2019 · Open Access · · DOI: https://doi.org/10.3390/math7080700 · OA: W2965535314

The k-generalized Fibonacci sequence ( F n ( k ) ) n (sometimes also called k-bonacci or k-step Fibonacci sequence), with k ≥ 2 , is defined by the values 0 , 0 , … , 0 , 1 of starting k its terms and such way that each term afterwards is the sum of the k preceding terms. This paper is devoted to the proof of the fact that the Diophantine equation F m ( k ) = m t , with t > 1 and m > k + 1 , has only solutions F 12 ( 2 ) = 12 2 and F 9 ( 3 ) = 9 2 .