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

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 Vincenzo Librandi Posts: 60 From: Rende - Cosenza - Italia Registered: 5/7/07
Re: x^2 - Ay^2 =1
Posted: May 12, 2007 5:02 AM

Philippe 92 wrote:

>>Seems the 3 other cases for A give the
>>fundamental solution.

Into Pell?s equation: x^2-Ay^2=1
If A=4n^2-n (with n integer >=1) then
y=64n-8, and x=128n^2-32n+1
A=(3,14,33,60,95,138,189,...,)
Y=(56,120,184,248,312,376,440,...,)
X=(97,449,1057,1921,3041,4417,6049,...,)
===============================

Into Pell?s equation: x^2-Ay^2=1
If A=4n^2+n (with n integer >=1) then
y=64n+8, and x=128n^2+32n+1
A=(5,18,39,68,105,150,203,...,)
Y=(72,136,200,264,328,392,456,...,)
X=(161,577,1249,2177,3361,4801,6497,...,)
=================================

Into Pell?s equation: x^2-Ay^2=1
If A=9n^2-8n+2 (with n integer >=0) then
y=27n-12, and x=81n^2-72n+17
A=(2,3,22,59,114,187,278,387,...,)
Y=(-12,15,42,69,96,123,150,177,...,)
X=(17,26,197,530,1025,1682,2501,3482,...,)
=================================

Into Pell?s equation: x^2-Ay^2=1
If A=9n^2-10n+3 (with n integer>=0) then
y=27n-15, and x=81n^2-90n+26
A=(3,2,19,54,107,178,267,374,...,)
Y=(-15,12,39,66,93,120,147,174,...,)
X=(26,17,170,485,962,1601,2402,3365,...,)
===============================

Into Pell?s equation: x^2-Ay^2=1
If A=121n^2-38n+3 (with n integer >=0) then
y= 1331n-209, and x=14641n^2-4598n+362
A=(3,86,411,978,1787,2838,...,)
Y=(-209,1122,2453,3784,5115,6446,...,)
X=(362,10405,49730,118337,216226,343397,...,)
=====================================

Into Pell?s equation: x^2-Ay^2=1
If A=121n^2-204n+86 (with n integer >=0) then
y=1331n-1122, and x=14641n^2-24684n+10405
A=(86,3,162,563,1206,2091,...,)
Y=(-1122,209,1540,2871,4202,5533,...,)
X=(10405,362,19601,68122,145925,253010,...,)
===================================

Talk to you soon.

Vincenzo Librandi
vincenzo.librandi@tin.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
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5/14/07 Iain Davidson
5/15/07 Philippe 92
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