Octic reciprocity

In number theory, octic reciprocity is a reciprocity law relating the residues of 8th powers modulo primes, analogous to the law of quadratic reciprocity, cubic reciprocity, and quartic reciprocity.

There is a rational reciprocity law for 8th powers, due to Williams.

to be +1 if x is a k-th power modulo the prime p and -1 otherwise.

Let p and q be distinct primes congruent to 1 modulo 8, such that

Then This number theory-related article is a stub.