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Fibonacci-type relations among solutions to the Pell equation. (English) Zbl 0765.11010

For the solutions to the Pell equation \(x^ 2-Dy^ 2=1\) three recursion possibilities having the form of generalized Fibonacci series are given. There are also asymptotic formulas and some further relationships between the solutions.

MSC:

11D09 Quadratic and bilinear Diophantine equations
11B39 Fibonacci and Lucas numbers and polynomials and generalizations
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