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Does anyone know of software (either commercial or free/open) that implements the general algorithm to solve quadratic diophantine equations as shown in this paper by Grunewald and Segal (2004), entitled 'On the integer solutions of quadratic equations'? http://thirdworld.nl/on-the-integer-solutions-of-quadratic-equations

melodrama
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  • Why do the program? Often you can record a parameterization of solutions in General. Depends on which equation you need to solve it. Formulate the question more specifically. – individ Jul 12 '16 at 04:27
  • I'm particularly interested in all finite solutions. The method linked above can give me all of those in general. My specific question is whether anyone knows of an implementation of that specific algorithm. – melodrama Jul 12 '16 at 17:03
  • Specify the question more clearly. And depending on the equation - write a specific formula. Even without the algorithm to do in some cases. – individ Jul 12 '16 at 17:16
  • I'm not interested in the handful of known special cases. I'm interested in the algorithm proved in that paper to solve the general case of quadratic equations. The question is straightforward. Is there software available that implements the algorithm described in the manuscript? I know that some special case is NP-Complete. If it's inefficient, that's okay. It is a tool that should exist. I am asking if it exists yet. – melodrama Jul 12 '16 at 21:34
  • Yes, of course - there. It is even possible to decide unambiguously and in a General way to record the decision. Depending on the equation formula can take many forms. Most often they are quite bulky. To make it easier to simplify and solve - it is necessary to know what form of the equation presented. – individ Jul 13 '16 at 04:22
  • OK, the general quadratic diophantine equation with 2 variables would be an example. – melodrama Jul 14 '16 at 01:57
  • If this equation has infinitely many solutions, then it will boil down to what is equivalent to the Pell equation. Generally speaking, the solvability of quadratic equations is determined by the existence of solutions of some Pell equations. Always this problem is reduced. For example. http://www.artofproblemsolving.com/community/c3046h1048219 – individ Jul 14 '16 at 04:24
  • @individ - I saw your post here: http://math.stackexchange.com/questions/580491/general-quadratic-diophantine-equation Do you have a suggestion for solving:

    9t-2rt-r-97=0

     – melodrama Jul 28 '16 at 01:55
  • This is not a quadratic equation. Select one variable and explore when you can be the solution. – individ Jul 28 '16 at 04:21

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