If there exists a rational integer x such that, when n, p, and q are positive integers, x^n congruent q (mod p), then q is the n-adic residue of p, i.e., q is an n-adic residue of p iff x^n congruent q (mod p) is solvable for x. Reciprocity theorems relate statements of the form "p is an n-adic residue of q" with reciprocal statements of the form "q is an n-adic residue of p."
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