Solving linear Diophantine equation and simultaneous linear Diophantine equations with minimum principles

Abstract

The all current methods of solving linear Diophantine equation and system of linear Diophantine equations have three shortcomings. Based on function thinking we put forward minimum principles to solve them, so that we can solve Generalized Chinese Remainder Problem easily. In order to discriminate accuracy of other methods, we propose basic solution system, the concept of transformation matrix and the concept of equivalence of basic solution systems for homogeneous linear indeterminate equations. This paper is also a classic example that mathematics problems for Post-graduate Students can be solved by only using middle school mathematics. We correct the misunderstanding for Cramer’s rule in mathematics circles too.