How to solve the equation $n^2 \equiv 0 \pmod{584}$?
You're looking for integers $k$ such that
$$n^2=2^373^1k $$
However, a number is a square iff all of its prime exponents are even. Thus $k$ must be of the form $$k=2 \cdot73 \cdot l^2$$ where $l $ is an arbitrary integer.
By taking the square root you will find that
$$n=2^2 \cdot 73^1 \cdot l $$
where $l \in \mathbb{Z}$.