## Mathematics, Department of

#### Date of this Version

1929

#### Abstract

If *p* be an odd prime, *q* is said to be an *n*- ic residue of *p* if the congruence *x*^{n} = *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.

## Comments

Published in

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