|
|
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
|
|
