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If p be an odd prime, q is said to be an n- ic residue of p if the congruence xn = q (mod p) has solutions; otherwise q is an n-ic non-residue of p. A necessary and sufficient condition that q be an n-ic residue of p is that
(1) q (p- 1)/δ ≡ 1, (mod p),
where δ = g.c.d. (p - 1, n). The numberf of n-ic residues of a given prime p is (p-1)/δ.
It is with the symmetric functions of these n-ic residues that this paper deals.