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A Family of Generalized Fibonacci and Lucas Numbers

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This Demonstration displays integer sequences of the form and , where and are the roots of the quadratic equation with integer coefficients and .

Contributed by: Abdulrahman Abdulaziz (June 2010)
Open content licensed under CC BY-NC-SA

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If and are integers, then the roots of the quadratic equation are and .

It turns out that produces a Lucas-like sequence, while produces a Fibonacci-like sequence. In particular, if , we obtain the Lucas and Fibonacci numbers.

Reference:

Integer Sequences of the Form a^n + b^n

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