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**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(m^{c} 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 2^{m+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 **|****sum**_{u in S, v in T} \chi (u+v)**|**^{2} \leq p **sum**_{u in S} 1 **sum**_{v 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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