I am trying to find a way of solving congruence systems of the form:
$$ b*x = a \quad mod \quad y $$
Where $b$ and $y$ are not prime to each other.
My current way of solving congruence systems where $b$ and $y$ are prime to each other is to find the multiplicative inverse of $b$ in $y$ and multiply $b$ (which will make it 1) and $a$ with this value.
$$ 13 \ x = 3 \ mod \ 17$$
I calculate the mul. inverse of 13 and multiply 3 and 13 times that value and thus I have solved this equation.
But I dont know how I can do that where $b$ and $y$ are not prime to each other.
$$3 x = 3 \ mod \ 9$$
How would I solve this ?