Solution of systems of linear Diophantine equations

Two new methods to solve linear systems of Diophantine equations are proposed - modular (CRT) and p-adic (Hensel). Each of them allows to obtain solutions of a system with the size n x m with the complexity O(n(beta) m). For quasi-square, systems, the p-adic method allows to obtain solution with the complexity O(n(3)), and the modular method with complexity O(n(beta +1)). Both estimates have the accuracy up to the logarithmic multipliers, being the power in the estimation of matrix multiplication time.