Fibonacci Numbers of the Forms PX2 ± 1, PX3 ± 1, Where P is Prime

Neville Robbins

A chapter in Applications of Fibonacci Numbers, 1988, pp 77-88 from Springer

Abstract: Abstract Let m denote a non-negative integer, Fm the mth Fibonacci number, p a prime. Fibonacci numbers of the forms x2, 2x2, x2+1, x2-1, px2, x3, 2x3, px3, p2x3, x3 ±1 have been studied by J. H. E. Cohn [1], R. Finkelstein [3], H. C. Williams [9], the author [7], [8], A. Petho [61, H. London & R. Finkelstein [5], and J. C. Lasarias & D. P. Weisser [4]. In this article, we find all solutions to each of the four equations: (A) $$ {F_m} = p{x^2} + 1 $$ (B) $$ {F_m} = p{x^2} - 1 $$ (C) $$ {F_m} = p{x^3} + 1 $$ (D) $$ {F_m} = p{x^3} - 1 $$

Date: 1988
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DOI: 10.1007/978-94-015-7801-1_9

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