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arXiv · 1304.1043

Solutions of the Pell equations x^2-(a^2+2a)y^2=N via generalized Fibonacci and Lucas numbers

Bilge Peker
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Abstract

In this study, we find continued fraction expansion of sqrt(d) when d=a^2+2a where a is positive integer. We consider the integer solutions of the Pell equation x^2-(a^2+2a)y^2=N when N={-1,+1,-4,+4}. We formulate the n-th solution (x_{n},y_{n}) by using the continued fraction expansion. We also formulate the n-th solution (x_{n},y_{n}) via the generalized Fibonacci and Lucas sequences.

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Bilge Peker. 2013-04-03. Solutions of the Pell equations x^2-(a^2+2a)y^2=N via generalized Fibonacci and Lucas numbers. https://arxiv.org/abs/1304.1043

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