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# Congruence Techniques for the Exact Solution of Integer Systems of Linear Equations

@article{Cabay1977CongruenceTF, title={Congruence Techniques for the Exact Solution of Integer Systems of Linear Equations}, author={S. Cabay and T. P. L. Lam}, journal={ACM Trans. Math. Softw.}, year={1977}, volume={3}, pages={386-397} }

- Published in ACM Trans. Math. Softw. 1977
DOI:10.1145/355759.355765

A new Fortran code, ESOLVE, is discussed for the exact solution of systems of linear equations with multiple-precision integer coefficients by congruence techniques. The code runs significantly faster than other codes which use congruential techniques. Test runs on two classes of problems reveal that the congruential method is competitive with the two-step multipleprecision method for solving integer systems exactly.