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x 2 − b 2 − b y 2 = N via Generalized Fibonacci
Bilge Peker,Hasan Senay +1 more
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TLDR
In this article, the integer solutions of the Pell equation x 2 − b 2 + b y 2 = N were considered and the n-th solution (xn,yn) was formulated in terms of generalized Fibonacci and Lucas sequences.Abstract:
In this study, we consider the integer solutions of the Pell equation x 2 − b 2 − b y 2 = N when N = {±1, ±4} and b is an integer with b ≥ 2. We formulate the n-th solution (xn,yn) in terms of generalized Fibonacci and Lucas sequences.read more
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Algorithmic Manipulation of Fibonacci Identities
TL;DR: In fact, all trigonometric identities can be derived from the basic identity sin2x cos2x = 1 as discussed by the authors, which is the same as the identity used in this paper.
Book
Beginning Number Theory
TL;DR: In this paper, a multi-disciplinary theory of citizenship is developed, exploring the human abilities needed for its practice and arguing that capitalism impedes the nurturing of these abilities, drawing on the work of a wide range of thinkers including Freud, Marx, Lacan, Habermas and Castells.