This is a problem about Diophantine equation.
The problem is the following.
If $ax+by=c$ is solvable and $b\ne0$, then prove that it has a solution $x_0$, $y_0$ with $0 \le x_0 <|b|$
First I thought that $x=x_1-\frac bg k$ , $y=y_1+\frac ag k$, where $g=gcd(a,b)$, $k$ is integer and $x_1$, $y_1$ is initial solution.
But, after this step, I am stuck and can't find what to do next.
Please help me solve this problem!!!