Polynomial algorithms for \(m\times (m+1)\) integer programs and \(m\times (m+k)\) diophantine systems (Q2265948)

Recent results \textit{R. Kannan} and \textit{A. Bachem} [SIAM J. Comput. 8, 499-507 (1979; Zbl 0446.65015)] (on computing the Smith Normal Form of a matrix) and \textit{H. W. Lenstra} [Math. Oper. Res. 8, 538-548 (1983; Zbl 0524.90067)] (on solving integer inequality systems) are used with classical results by H. J. S. Smith (1861) to obtain polynomial-time algorithms for solving \(m\times (m+1)\) equality constrained integer programs and \(m\times (m+k)\) systems of diophantine equations for fixed k.