On Fibonacci Numbers Which Are Powers: II

Neville Robbins · The Fibonacci Quarterly · 1983

where Fm denotes the 77?th Fibonacci number, and o > 1. Without loss of generality , we may require that t be prime. The unique solution for t 2, namely (m, c) = (12, 12)5 was given by J. H. E. Cohn [2], and by 0. Wyler [11]. The unique solution for £ = 3, namely (m9 o) = (6, 2), was given by H. London and R. Finkelstein [5] and by J. C. Lagarias and D. P. Weisser [4]. A. Petho [6] showed that (#) has only finitely many solutions with t > 1, where mscs t all vary. In fact, he shows that all solutions of (#) can be effectively determined; that is, there is an effectively computable bound B such that all solutions of (*) have

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