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:
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