Talk:Fibonacci pseudoprime

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I dont understand the defintion of U and V, what are the a's and the b's and how are they related to P and Q?

First: Your Fibonacci pseudoprimes are Lucas pseudoprimes, because the Sequence is the Lucas Sequence (2, 1, 3, 4, 7, 11, 18, 29, ...).
Second: An answer of the Question:
You have a quadratic Equation x2 + Px + Q = 0. a and b are the two Solutions of this quadratich Equation, you can solve with the PQ-Method.
With this two Solutions a and b in relation to P and Q, you can build two kinds of Sequences:
Kind A: U_n(P,Q) = \frac{a^n-b^n}{a-b}
and
Kind B: Vn(P,Q) = an − bn
The Fibonacci sequence (0, 1, 1, 2, 3, 5, 8, 13, 21, ...) is a special form of the generalized lucas sequence U_n(1,-1) = \frac{a^n-b^n}{a-b} with a = \frac{1 + \sqrt{5}}{2} and b = \frac{1 - \sqrt{5}}{2}.
The co-sequence (2, 1, 3, 4, 7, 11, 18, 29, ...) to the Fibonacci Sequence, which is also called as Lucas sequence, is the second Kind of the generalized Lucas sequence Vn(1, − 1) = an − bn with the same solutions a = \frac{1 + \sqrt{5}}{2} and b = \frac{1 - \sqrt{5}}{2}. --217.233.227.74 20:12, 11 Dec 2004 (UTC) (User:Arbol01 in de.wikipedia.org).
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