For what odd prime p is -3 a quadratic residues? Non-residue? For what odd prime p is -3 a quadratic residues? Non-residue?


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*Having a bit of trouble with this question, we are currently covering a section  on quadratic reciprocity and didn't really see anything in my notes that helped me solve this. Any help is greatly appreciated.


Hint: use the Legendre symbol. Then you have that $(\frac{-3}{p})=(\frac{-1}{p})(\frac{3}{p})$, and use what you know about $(\frac{-1}{p})$ and quadratic reciprocity.
