arXiv:1304.1043 Abstract | arXiv Analytics

arXiv:1304.1043 [math.NT]Abstract References Reviews Resources

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

Published 2013-04-03Version 1

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.

Comments: 5 pages. arXiv admin note: substantial text overlap with arXiv:1303.1838

Categories: math.NT

Subjects: 11D09, 11D79, 11D45, 11A55, 11B39, 11B50, 11B99

Keywords: pell equation, generalized fibonacci, lucas numbers, continued fraction expansion, n-th solution

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