Some new residuacity criteria

Abstract

Let e and k be integers>2 with e odd and k even. Set 2 / = L. C. M. (e, k) and let p be a prime with p = 1 (mod 2/) having ^ as a primitive root. It is shown that the index of e (with respect to g) modulo k can be computed in terms of the cyclotomic numbers of order /. By applying this result