Talk:Lucas sequence

Equality

$V_{p}(a_{2}+1,a_{2})\equiv V_{1}(a_{2}+1,a_{2})$ is equal to $a_{2}^{p}\equiv a_{2}\mod p$

Proof:

$a={\frac {P+{\sqrt {P^{2}-4Q}}}{2}}$ and $b={\frac {P-{\sqrt {P^{2}-4Q}}}{2}}$

$P=(a_{2}+1)\$ and $Q=a_{2}\$

$a={\frac {(a_{2}+1)+{\sqrt {(a_{2}+1)^{2}-4a_{2}}}}{2}}={\frac {2a_{2}}{2}}=a_{2}$

$b={\frac {(a_{2}+1)-{\sqrt {(a_{2}+1)^{2}-4a_{2}}}}{2}}={\frac {2}{2}}=1$

Follows:

$V_{n}(a_{2}+1,a)=a_{2}^{n}+1\$

follows:

$V_{p}(a_{2}+1,a)-V_{1}(a_{2}+1,a)=a_{2}^{p}+1-(a_{2}+1)=a_{2}^{p}-a_{2}\$

--arbol01 21:33, 15 November 2007 (CST)

Improvement of readability

Please do not be offended, but this article was not so readable due to the poor use of English. I've that to help improve the presentation in this article. --Hendra 08:34, 17 November 2007 (CST)