n-reciprocity

[mitchell2007]

generalizing Gauss and others results could we speak of a nreciprocity involving teh solution (p and q are distinct primes) of x^{n} \equiv p mod (q) and x^{n} \equiv q mod (p ) where n is every positive integer.

[DeadWolfe]

http://mathworld.wolfram.com/ReciprocityTheorem.html