Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.

Topic: x^2 - Ay^2 =1
Replies: 125   Last Post: Jun 28, 2007 2:32 PM

 Messages: [ Previous | Next ]
 Vincenzo Librandi Posts: 60 From: Rende - Cosenza - Italia Registered: 5/7/07
Re: x^2 - Ay^2 =1
Posted: May 14, 2007 4:15 PM

On May 12, 8:07 pm, Vincenzo Librandi <vincenzo.librandw...@alice.it>
wrote:
> You ask me the form
> X^2-3*Y^2=1, then see this:
>
> 2^2-3*1=1
> 7^2-3*4^2=1
> 26^2-3*15^2=1
> 97^2-3*56^2=1
> 362^2-3*209^2=1
> 1351^2-3*780^2=1
> 5042^2-3*2911^2=1
> 18817^2-3*10864^2=1
> 70226^2-3*40545^2=1
> 262087^2-3*151316^2=1
> 978122^2-3*564719^2=1
> 3650401^2-3*2107560^2=1
> 13623482^2-3*7865521^2=1
> 50843527^2-3*29354524^2=1
> 189750626^2-3*109552575^2=1
>
> and so on for infinite, and for A.
>
> Ask and invite to find my metod.

>>Gerry wrote:
>>
>>Hi Vincenzo,
>>There are more methods.
>>You can find them at :
>>

http://www.research.att.com/~njas/sequences/?q=2%2C7%2C26%2C97&language=english
>>Sequence : A001075
>>a(n) = ((2+sqrt(3))^n + (2-sqrt(3))^n)/2=1, 2, 7, 26, 97, 362, 1351,
>>5042, 18817, 70226,...

Hi Gerry,
Isn?t my use to copy formula, therefore I don?t use
any formule, neither so much less to sequence A001075.
I?m serching for the solution of Pell?s equatione:
X^2-AY^2=1, without the antiquated metod, how the
continuos fractions and continuos square.

My metod for this chance is very easy.
Having the primitive: 2^2-3*1^2 = 1

The sequence for x are:
2*4-1=7
7*4-2=26
26*4-7=97
97*4-26=362
362*4-97=1351
1351*4-362=5042
5042*4-1351=18817
18817*4-5042=70226
And so on

You understand Gerry ? It?s very easy ?

The sequence for y are:
1*4-0=4
4*4-1=15
15*4-4=56
56*4-15=209
209*4-56=780
780*4-209=2911
2911*4-780=10864
10864*4-2911=40545
40545*4-10864=151316
And so on

Easier and easier !

Regards
Vincenzo Librandi
vincenzo.librandweoz@alice.it

Date Subject Author
5/10/07 Vincenzo Librandi
5/10/07 Philippe 92
5/10/07 Vincenzo Librandi
5/10/07 Philippe 92
5/11/07 Vincenzo Librandi
5/11/07 Philippe 92
5/13/07 Iain Davidson
5/12/07 Vincenzo Librandi
5/17/07 Philippe 92
5/12/07 Vincenzo Librandi
5/13/07 Gerry
5/14/07 Philippe 92
5/14/07 Vincenzo Librandi
5/17/07 Philippe 92
5/14/07 Vincenzo Librandi
5/14/07 Iain Davidson
5/15/07 Philippe 92
5/16/07 Vincenzo Librandi
5/17/07 Philippe 92
5/16/07 Gerry
5/16/07 Philippe 92
5/16/07 Vincenzo Librandi
5/17/07 Philippe 92
5/17/07 Vincenzo Librandi
5/17/07 Iain Davidson
5/17/07 Philippe 92
5/17/07 Iain Davidson
5/19/07 Philippe 92
5/19/07 Vincenzo Librandi
5/19/07 Philippe 92
5/20/07 Vincenzo Librandi
5/20/07 Philippe 92
5/20/07 Iain Davidson
5/20/07 Philippe 92
5/20/07 Iain Davidson
5/20/07 Philippe 92
5/21/07 Iain Davidson
5/22/07 Philippe 92
5/22/07 Iain Davidson
5/23/07 Gerry
5/23/07 Philippe 92
5/24/07 Gerry
5/24/07 Gerry
5/24/07 Iain Davidson
5/25/07 Gerry
5/25/07 Iain Davidson
5/23/07 Philippe 92
5/24/07 Iain Davidson
5/25/07 Philippe 92
5/26/07 Iain Davidson
5/17/07 Philippe 92
5/22/07 Vincenzo Librandi
5/24/07 Vincenzo Librandi
5/25/07 Gerry
5/26/07 Vincenzo Librandi
5/26/07 Philippe 92
5/26/07 Phil Carmody
5/26/07 Philippe 92
5/26/07 Vincenzo Librandi
5/27/07 Philippe 92
5/27/07 Vincenzo Librandi
5/27/07 Philippe 92
5/28/07 Vincenzo Librandi
5/28/07 Philippe 92
5/28/07 Vincenzo Librandi
5/28/07 Philippe 92
5/28/07 Vincenzo Librandi
5/29/07 Philippe 92
5/29/07 Vincenzo Librandi
5/29/07 Philippe 92
5/29/07 Vincenzo Librandi
5/29/07 Philippe 92
5/25/07 Philippe 92
5/26/07 Vincenzo Librandi
5/27/07 Vincenzo Librandi
5/27/07 Philippe 92
5/29/07 Vincenzo Librandi
5/29/07 Philippe 92
5/29/07 Vincenzo Librandi
5/30/07 Vincenzo Librandi
5/31/07 Philippe 92
5/31/07 Vincenzo Librandi
5/30/07 Vincenzo Librandi
5/31/07 Vincenzo Librandi
6/1/07 Vincenzo Librandi
6/1/07 Vincenzo Librandi
6/1/07 Vincenzo Librandi
6/2/07 Philippe 92
6/2/07 Vincenzo Librandi
6/3/07 Vincenzo Librandi
6/3/07 Vincenzo Librandi
6/4/07 Philippe 92
6/4/07 Vincenzo Librandi
6/2/07 Vincenzo Librandi
6/4/07 Vincenzo Librandi
6/5/07 Vincenzo Librandi
6/6/07 Vincenzo Librandi
6/7/07 Philippe 92
6/7/07 Vincenzo Librandi
6/7/07 Vincenzo Librandi
6/7/07 Vincenzo Librandi
6/7/07 Philippe 92
6/8/07 Vincenzo Librandi
6/8/07 Philippe 92
6/9/07 Vincenzo Librandi
6/10/07 Vincenzo Librandi
6/10/07 Vincenzo Librandi
6/10/07 Philippe 92
6/10/07 Vincenzo Librandi
6/10/07 Vincenzo Librandi
6/10/07 Philippe 92
6/11/07 Vincenzo Librandi
6/11/07 Philippe 92
6/10/07 Philippe 92
6/11/07 Vincenzo Librandi
6/11/07 Philippe 92
6/11/07 Vincenzo Librandi
6/12/07 Vincenzo Librandi
6/12/07 Philippe 92
6/13/07 Vincenzo Librandi
6/14/07 Vincenzo Librandi
6/14/07 Vincenzo Librandi
6/17/07 Vincenzo Librandi
6/23/07 Vincenzo Librandi
6/28/07 Vincenzo Librandi
6/17/07 Vincenzo Librandi