Diophantine Linear System Solving

Abstract

A simple randomized algorithm is given for finding an integer solution to a system of linear Diophantine equations. Given as input a system which admits an integer solution, the algorithm can be used to find such a solution with probability at least 1/2. The running time (number of bit operations) is essentially cubic in the dimension of the system. The analogous result is presented for linear systems over the ring of polynomials with coefficients from a field.