Symmetric Functions of n-IC Residues (mod p)

Authors

• T. A. Pierce, University of Nebraska - Lincoln

Document Type

Article

Date of this Version

1929

Comments

Published in Bull. Amer. Math. Soc. 35 (1929) 708-710. Used by permission.

Abstract

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.