Neil Sloane on Wed, 04 Jun 2014 02:45:40 +0200

[Date Prev] [Date Next] [Thread Prev] [Thread Next] [Date Index] [Thread Index]

Numbers represented by indefinite binary quad. forms

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!
Neil Sloane