# Chinese Remainder Theorem (I think?)

Given system of congruences,

$$x^3 \equiv y_1 \mod n_1$$
$$x^3 \equiv y_2 \mod n_2$$
$$x^3 \equiv y_3 \mod n_3$$

You are given $$y_1, y_2, y_3, n_1, n_2, n_3$$. The $$n_i$$'s are pairwise relatively prime. Solve for x.

I think there might be a connection between the fact that the exponent of x is 3 and there are 3 congruences given. But I haven't the slightest idea how to approach.

For each of them you also know there exists a d such that $$y_i^d \equiv x \mod n_i$$ but I don't think that is so useful.