Solving a system of diophantine equations with lower and upper bounds on the variables

@inproceedings{Aardal1998SolvingAS,
  title={Solving a system of diophantine equations with lower and upper bounds on the variables},
  author={Karen Aardal},
  year={1998}
}
We develop an algorithm for solving a system of diophantine equations with lower and upper bounds on the variables. The algorithm is based on lattice basis reduction. It rst nds a short vector satisfying the system of diophantine equations, and a set of vectors belonging to the null-space of the constraint matrix. Due to basis reduction, all these vectors are relatively short. The next step is to branch on linear combinations of the null-space vectors, which either yields a vector that satis es… CONTINUE READING

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