Questions on the use of Mathematica to find integer/rational solutions to equations.

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5
votes
0answers
84 views

Find out whether solutions exist rather than full-blown solution search

I have some quadratics, and I am trying to find out whether there exist solutions in the integers. The following tells me that the first does, wheraeas the second doesn't: ...
5
votes
0answers
335 views

Computing Ehrhart's polynomial for a convex polytope

Is there a Mathematica implementation for computing the Ehrhart polynomial of a convex polytope which is specified either by its vertices or by a set of inequalities? I am interested in knowing this ...
3
votes
0answers
171 views

Solving Thue equations

A Thue equation is a 2-variable homogeneous integer polynomial of degree at least 3. It's well-known that such equations have only finitely many solutions over the integers. I'm trying to solve some ...
0
votes
0answers
3 views

diophantine linear equation with condition on the sum of coefficients

I am trying to solve the following diophantine equation x*a + y*b == c where a,b,c are integers and the absolute value of their sums is, for instance, 4. Then I ...