## Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  079.06304
Autor:  Erdös, Paul; Shapiro, Harold N.
Title:  On the least primitive root of a prime. (In English)
Source:  Pac. J. Math. 7, 861-865 (1957).
Review:  Let g(p) be the least positive primitive root of a prime p. The authors prove that g(p) = O(mc p ½) where c is a constant and m is the number of distinct prime factors of p-1. As m large, it is an improvement of a result of the reviewer: g(p) \leq 2m+1 p ½. The authors introduce a lemma and then apply Brun's method to obtain the result. The lemma runs as following: Let S and T be two sets with distinct integers, mod p. Then for any non-principal character \chi, we have

|sumu in S, v in T \chi (u+v)|2 \leq p sumu in S 1 sumv in T 1.

Reviewer:  L.K.Hua
Classif.:  * 11N69 Distribution of integers in special residue classes
11A07 Congruences, etc.
Index Words:  Number Theory

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