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Questions tagged [diophantine-equation]

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How do you solve a general linear diophantine equation in polynomial time (with minimization constraint)?

Given $$ a_1 X_1 + \dots + a_n X_n = b $$ where $a_i, b \in \Bbb{Z}$. How do you come up with a clearer picture of the solution set in polynomial time. Also, what I really want is to do the above,...
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Multivariate polynomials

Given a Diophantine equation $p(x_1,x_2,...,x_n)$, Can I find a reduction from $\text{dioph}(\mathbb{N}) \leq \text{dioph}(\mathbb{N}_e)$? $\mathbb{N}_e$ is the set of even numbers. So I have to ...
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Solution to Diophantine equations

I am trying to solve a problem that boils down to finding the number of solutions of a linear Diophantine equation with restrictions. To be precise for equations : $ax + by + cz = k$ and $x + y + z =...