Bilge Peker, Hasan Senay
Published 2013-03-07Version 1
In this study, we find continued fraction expansion of sqrt(d) when d=a^2b^2-b and d=a^2b^2-2b where a and b are positive integers. We consider the integer solutions of the Pell equations x^2-(a^2b^2-b)y^2=N and x^2-(a^2b^2-2b)y^2=N when N is {+-1,+-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}) in terms of generalized Fibonacci and Lucas sequences.
Solutions of the Pell equations x^2-(a^2+2a)y^2=N via generalized Fibonacci and Lucas numbers
The first and second moment for the length of the period of the continued fraction expansion for $\sqrt{d}$
Generalized Fibonacci and Lucas Numbers of the form $5x^{2}$
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