I would like to show that Euler's and Legendre's formulations of the Law of Quadratic Reciprocity are equivalent:
Where Euler's version of the law of quadratic reciprocity is
(a/p) = (a/q),
with p and odd prime, a not divisible by p, and q a prime with p = +- q (mod 4a).
And Legendre's version is
(p/q)(q/p) = (-1) ^ ((p-1)/2)*((q-1)/2),
where p and q are distinct odd primes.
How do I approach this?