Suppose I want to find the smallest $x$ that satisfies the following set of equations:
$$ \left(x+a_1\right)\mod{d_1} \not\equiv 0 \\ \left(x+a_2\right)\mod{d_2} \not\equiv 0 \\ \left(x+a_3\right)\mod{d_3} \not\equiv 0 \\ \vdots $$
Is there a way to systematically do this? Thanks.
