Max Alekseyev on Thu, 20 Nov 2008 00:29:34 +0100

 Pell's equations and beyond

• To: pari-users <pari-users@list.cr.yp.to>
• Subject: Pell's equations and beyond
• From: "Max Alekseyev" <maxale@gmail.com>
• Date: Wed, 19 Nov 2008 15:26:57 -0800
• Delivery-date: Thu, 20 Nov 2008 00:29:34 +0100
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```Dear pari-users,

bivariate Diophantine equation solver:
in PARI/GP. Is anything like that already present there?
At the moment, I'm not even sure if there is a simple way to solve
Pell's equations in PARI/GP.

Could you please clarify what is the best way (and if there exists one
without much programming) to solve the following equations in PARI/GP:

1) Pell's equation x^2 - D y^2 = 1, where D is integer ?

2) Generalized Pell's equation x^2 - D y^2 = c, where D and c are integer ?

3) Quadratic bivariate Diophantine equation in the general form: ax^2
+ bxy + cy^2 + dx + ey + f = 0, where a,b,c,d,e,f are integer
coefficients ?

Thanks,
Max

```