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).