# [seqfan] Re: Finding numbers represented by indefinite binary quadratic forms

apovolot at gmail.com apovolot at gmail.com
Wed Jun 4 14:39:18 CEST 2014

```It worked for me

x2 + 3 xy - 3 y2 - 15 = 0

X0 = 3
Y0 = 1

and also:
X0 = -3
Y0 = -1

and also:
X0 = -3
Y0 = -1

and also:
X0 = 3
Y0 = 1

and also:
X0 = 6
Y0 = 7

and also:
X0 = -6
Y0 = -7

and also:
X0 = -3
Y0 = -2

and also:
X0 = 3
Y0 = 2

and also:
X0 = 6
Y0 = -1

and also:
X0 = -6
Y0 = 1

and also:
X0 = 3
Y0 = 2

and also:
X0 = -3
Y0 = -2

Xn+1 = P Xn + Q Yn
Yn+1 = R Xn + S Yn

Xn+1 = P Xn + Q Yn
Yn+1 = R Xn + S Yn

P = 1
Q = 3
R = 1
S = 4

as well as

P = 4
Q = -3
R = -1
S = 1

------------

> On Jun 4, 2014, at 8:20 AM, Neil Sloane <njasloane at gmail.com> wrote:
>
> Max, Thanks for that link! I tried entering
> 1
> 3
> -3
> 0
> 0
> -15
> but that seems to have killed the website. I agree that it doesn't always
> work!
>
> Best regards
> Neil
>
>
>> On Wed, Jun 4, 2014 at 7:42 AM, Max Alekseyev <maxale at gmail.com> wrote:
>>
>> There is an online solver for this kind of equaitons by Dario Alpern:
>> (which however does not always work correctly)
>>
>> Regards,
>> Max
>>
>>
>>> On Wed, Jun 4, 2014 at 12:41 AM, Neil Sloane <njasloane at gmail.com> wrote:
>>> Does anyone have a program for doing the following:
>>>
>>> Given an indefinite binary quadratic form ax^2+bxy+cy^2 (with
>> discriminant
>>> b^2-4ac>0 and not a square) and a positive or negative number n, decide
>> if
>>> ax^2+bxy+cy^2 = n has a solution.
>>>
>>> (If n = p is a prime, one can use the PARI command
>> qfbsolve(Qfb(a,b,c),p) )
>>>
>>> Neil
>>>
>>> _______________________________________________
>>>
>>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>
>
>
> --
> Dear Friends, I have now retired from AT&T. New coordinates:
>
> Neil J. A. Sloane, President, OEIS Foundation
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.