Finding possible solutions to a modular arithmetic question.

Question

How many solutions does the quadratic equation $\bar{x^{2}}= \bar{2}$ have in $\mathbb{z}_{47}$? The only way i can think of doing this is computing all the squares within the modulo. But i know there is a quicker way just don't know what this would be?

Answer 1

Quadratic reciprocity was made to answer exactly this kind of question. In your case you can use the supplements.