Suppose we had a list of modular expressions as follows:
$$ y_0 \equiv s_0 \mod r_0 $$
$$ y_0 \equiv s_1 \mod r_0-1 $$
$$ y_0 \equiv s_2 \mod r_0-2 $$
$$ y_0 \equiv s_3 \mod r_0-3 $$
$$ y_0 \equiv s_n \mod r_0-n $$
We could find the modular equation for any $n$. Is there a way to solve for $y_0$?
update That is to say, for every equation we would know the value of $s_n$ and $r_0$, but $y_0$ is unknown.