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Questions tagged [diophantine-equations]

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

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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 ...
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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 ...
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Introducing constraints in FrobeniusSolve

I have a knapsack problem. Say I have N possible items $x_i$. I would like to know: $ \sum_{i=0}^{2} c_i x_i = W$ With the following constraint: $c_i=3 \lor 4$ As an example suppose the set $x_i=...
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How to test solvability of a Diophantine equation?

When applying the BRC theorem I need to test if an equation has a non-zero solution in integers. The equation is of form: $$x^2 + by^2 + cz^2 = 0$$ We could try to directly check if this equation ...
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When can FindInstance prove no solutions for a nonlinear Diophantine equation?

A few months ago, I thought of a marvelous proof that $a^3+b^3=2c^3$ has no nontrivial integer solutions in $\mathbb{N}$, but the margin of my cocktail napkin was too small to contain it. Now I've ...