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.
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...