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Re: x^2 - Ay^2 =1
Posted:
Jun 14, 2007 1:34 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
**************************************
(13)
If A=(n^2-1)/4^2, y=4, x=n
(with n>=9 and n^2-1=0 mod.4^2)
n=(9,15,17,23,25,31,33,39,...,)
A=(5,14,18,33,39,60,68,95,...,)
Y=(4,4,4,4,4,4,4,4,...,)
X=(9,15,17,23,25,31,33,39,...,)
**************************************
(14)
If A=(n^2+2)/9^2, y=9n, x=n^2+1)
(with n>=59 and n^2+2=0 mod.9^2)
n=(59,103,140,184,221,...,)
A=(43,131,242,418,603,...,)
Y=(531,927,1260,1656,1989,...,)
X=(3482,10610,19601,33857,48842,...,)
**************************************
(15)
If A=(n^2-1)/30^2, y=30, x=n
(with n>=199 and n^2-1=0 mod.30^2)
n=199,251,449,451,649,701,...,)
A=(44,70,224,226,468,546,...,)
Y=(30,30,30,30,30,30,...,)
X=(199,251,449,451,649,701,...,)
**************************************
(16)
If A=(n^2-2)/23^2, y=23n, x=n^2-1
(with n>=156, and n^2-2=0 mod.23^2)
n=(156,373,685,902,1214,1431,...,)
A=(46,263,887,1538,2786,3871,...,)
Y=(3588,8579,15755,20746,27922,32913,...,)
X=(24335,139128,469224,813603,1473795,2047760,)
************************************************
(17)
If A=(n^2-1)/90^2, y=90, x=n
(with n>=649 and n^2-1=0 mod 90^2)
n=(649,3401,4049,4051,4699,...,)
A=(52,1428,2024,2026,2726,...,)
Y=(90,90,90,90,90,...,)
X=(649,3401,4049,4051,4699,...,)
***************************************
(18)
If A=(n^2+1)/25^2, y=50n, x=2n^2+1
(with n>=182, and n^2+1 =0 mod.25^2)
n=(182,443,807,1968,1432,1693,...,)
A=(53,314,1042,1825,3281,4586,...,)
Y=(9100,22150,40350,53400,71600,84650,...,)
X=(66249,392499,1302499,2281249,4101249,5732499,,,)
***************************************************
continued
Regards
Vincenzo Librandi
vincenzo.librandi@tin.it
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