Задача 13.

Let $(x_0,y_0)$ be a solution of the following equation \begin{equation*} ax+by=d. \end{equation*} Let $a_0$ and $b_0$ be numbers such that $GCD(a,b)a_0=a$, $GCD(a,b)b_0=b$. Show that each solution of equation $ax+by=d$ has the following form \begin{equation*} x=x_0+b_0t,  y=y_0-a_0t, \end{equation*} where $t\in\mathbb Z$.