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Re: x^2 - Ay^2 =1
Posted:
May 17, 2007 6:24 AM
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Vincenzo Librandi wrote :
>
> Into Pell's equation: x^2-Ay^2=1
> If A= 25n^2-14n+2 (with n integer >=0) then
> y=250n-70, and x=1250n^2-700n+99
may be OK only for n>=1
> ===================================
>
> Into Pell's equation: x^2-Ay^2=1
> If A= 25n^2-36n+13 (with n integer >=0) then
> y=250n-180, and x=1250n^2-1800n+649
may be OK only for n != 1
> ==============================
>
> Into Pell's equation: x^2-Ay^2=1
> If A= 25n^2-2n (with n integer >=1) then
> y=250n-10, and x=1250n^2-100n+1
False.
The fundamental solution is
X0 = 25n - 1, Y0 = 5
the CF expansion is [5n-1,1,3,1,10n-2,1,3,1,10n-2...]
> ===================================
>
> Into Pell's equation: x^2-Ay^2=1
> If A= 25n^2+2n (with n integer >=1) then
> y=250n+10, and x=1250n^2+100n+1
False
The fundamental solution is
X0 = 25n+1, Y0 = 5
The CF expansion is [5n,5,10n,5,10n...]
> ===================================
>
> To continue......
... this endless list of specific cases.
No finite set of quadratic forms can cover the full set of integers.
Regards.
--
Philippe C., mail : chephip+news@free.fr
site : http://chephip.free.fr/ (recreational mathematics)
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