Parametric Solutions of System of Linear Diophantine Equations by Crushing Method
P. Anuradha Kameswari *
Department of Mathematics, Andhra University, Visakhapatnam - 530003, Andhra Pradesh, India.
Aweke Belay
Department of Mathematics, Andhra University, Visakhapatnam - 530003, Andhra Pradesh, India.
*Author to whom correspondence should be addressed.
Abstract
There are studies on parametric solutions of system of Linear Diophantine equations based on uni-modular reductions of the coefficient matrix. In this paper we generate parametric solutions, with uni-modular row reductions on the coefficient matrix, based on the steps used in obtaining gcd of the coefficients in a row by crushing method. This application of gcd by crushing specifies an order for the row reductions and enables to give algorithm for the computations.
Keywords: Diophantine equations, parametric solutions