Integral Solutions to Linear Indeterminate Equation

Abstract

In this paper, using Euler's function, we give a formula of all integral solutions to linear indeterminate equation with $s$-variables $a_1{x}_1+a_2{x}_2+...+a_s{x}_s=n$. It is a explicit formula of the coefficients $a_1$, $a_2$,..., $a_s$ and the free term $n$.