منابع مشابه
On Fibonacci Powers
Fibonacci numbers have engaged the attention of mathematicians for several centuries, and whilst many of their properties are easy to establish by very simple methods, there are several unsolved problems connected to them. In this paper we review the history of the conjecture that the only perfect powers in Fibonacci sequence are 1, 8, and 144. Afterwards we consider more stronger conjecture an...
متن کاملOn the Fibonacci length of powers of dihedral groups
For a finitely generated group G = 〈A〉, where A = {a1, a2, . . . , an}, the sequence xi = ai, 1 ≤ i ≤ n, xi+n = ∏n j=1 xi+j−1, i ≥ 1, is called the Fibonacci orbit of G with respect to the generating set A, denoted FA(G). If FA(G) is periodic we call the length of the period of the sequence the Fibonacci length of G with respect to A, written LENA(G). In this paper we examine the Fibonacci leng...
متن کاملSmall Prime Powers in the Fibonacci Sequence
It is shown that there are no non-trivial fifth-, seventh-, eleventh-, thirteenthor seventeenth powers in the Fibonacci sequence. For eleventh, thirteenthand seventeenth powers an alternative (to the usual exhaustive check of products of powers of fundamental units) method is used to overcome the problem of having a large number of independent units and relatively high bounds on their exponents...
متن کاملOn Fibonacci Numbers Which Are Powers: I I
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 ...
متن کاملIndependent subsets of powers of paths, and Fibonacci cubes
We provide a formula for the number of edges of the Hasse diagram of the independent subsets of the hth power of a path ordered by inclusion. For h = 1 such a value is the number of edges of a Fibonacci cube. We show that, in general, the number of edges of the diagram is obtained by convolution of a Fibonacci-like sequence with itself.
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ژورنال
عنوان ژورنال: Publikacije Elektrotehnickog fakulteta - serija: matematika
سال: 2006
ISSN: 0353-8893
DOI: 10.2298/petf0617038a