Talk:Fibonacci pseudoprime

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 $x^2+Px+Q=0$. 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: $V_n(P,Q)=a^n-b^n$

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 $V_n(1,-1)=a^n-b^n$ 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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