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Re: x^2 - Ay^2 =1
Posted:
Jun 17, 2007 12:13 PM
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continued...
Hi,
we will give to all the polinomials formulas that
give the primitive of Pell's equation x^2-Ay^2=1
**************************************
(19)
If A=(n^2-1)/12^2, y=12, x=n
(with n>=89 and n^2-1=0 mod.12^2)
n=(89,127,143,145,...,)
A=(55,112,142,146,...,)
Y=(12,12,12,12,...,)
X=(89,127,143,145,...,)
****************************************
(20)
If A=(n^2-1)/20^2, y=20, x=n
(with n>=151 and n^2-1=0 mod.20^2)
n=(151,201,351,...,)
A=(57,101,308,...,)
Y=(20,20,20,...,)
X=(151,201,351,...,)
*****************************************
(21)
If A=(n^2+1)/3805^2, y=7610n, x=2n^2+1
(with n>=29718 and n^2+1=0 mod.3805^2
n=29718
A=61
Y=1766319049
X=226153980
-----------
n=5241807
A=1897810
Y=39890151270
X=54953081250499
-----------------
n=9236218
A=5892221
Y=70287618980
X=170615445887049
-----------------
n=14448307
A=14418650
Y=109951616270
X=417507150332499
****************************************
(22)
If A=(n^2+2)/27^2, y=27n, x=n^2+1
(with n>=221 and n^2+2=0 mod.27^2)
n=(221,508,950,1237,1679,...,)
A=(67,354,1238,2099,3867,...,)
Y=(5967,13716,25650,33399,45333,...,)
X=(48842,258065,902501,1530170,2819042,..,)
********************************************
(23)
If A=(529n^2+23)/36^2, y=72n, x=46n^2+1
(with n>=13 and 529n^2+23=0 mod.36^2)
n=13, A=69,Y=936,X=7775.
*******************************************
(24)
If A=(n^2+1)/125^2, y=250n, x=2n^2+1
(with n>=1068 andn^2+1=0 mod.125^2)
n=(1068,14557,16693,30182,...,)
A=(73,13562,17784,58301,...,)
Y=(267000,3639250,4173250,7545500,...,)
X=(2281249,423812499,557312499,1821906249,.,)
********************************************
continued ...
Regards
Vincenzo Librandi
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