1. ## Legendre symbol proof

Prove that if p>3 is an odd prime, then (-3/p) = 1 if p==1(mod 6) and -1 if p==5(mod 6). Note that (-3/p) is the Legendre symbol, not division. Thank you.

2. It's a direct application of quadratic reciprocity!

3. Can you get me started on the proof? I know that the Law of Quadratic Reciprocity states that if p and q are odd primes and p==q==3(mod 4), then (p/q) = -(q/p). Otherwise, (p/q) = (q/p). But I am not seeing an instant connection to mod 6...

4. Another way of writing the law of quadratic reciprocity is

$\left(\frac{p}{q}\right)\left(\frac{q}{p}\right)=(-1)^{(p-1)(q-1)/4}$.

See what you get from there!