What is N-Reciprocity and its significance in number theory?

[mitchell2007]

generalizing Gauss and others results could we speak of a nreciprocity involving the 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