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).

Start a discussion about improving the Fibonacci pseudoprime page

Talk pages are where people discuss how to make content on Wikipedia the best that it can be. You can use this page to start a discussion with others about how to improve the "Fibonacci pseudoprime" page.

Start a discussion