Neil Sloane on Wed, 04 Jun 2014 02:45:40 +0200
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Numbers represented by indefinite binary quad. forms
- To: pari <email@example.com>
- Subject: Numbers represented by indefinite binary quad. forms
- From: Neil Sloane <firstname.lastname@example.org>
- Date: Tue, 3 Jun 2014 20:45:32 -0400
- Delivery-date: Wed, 04 Jun 2014 02:45:40 +0200
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Given an indefinite binary quadratic form ax^2+bxy+cy^2 (with discriminant b^2-4ac>0 and not a square) and a number n, how to use PARI to see if ax^2+bxy+cy^2=n has a solution?
[Back in 2003 Bill Alombert said: I have added a new function qfbsolve. qfbsolve(Q,p): Solve the equation Q(x,y) = p over the integers, where Q is an imaginary binary quadratic form and p a prime number. Return [x,y] as a two-components vector, or zero if there is no solution. Note that this functions return only one solution and not all the solutions. This is a preliminary implementation. I plan to allow non prime p and real binary quadratic. Me: Does the "non-prme" version exist? - that would solve my problem!