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# 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} }

- Published 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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