On the distribution of consecutive square-free primitive roots modulo p

A positive integer n is called a square-free number if it is not divisible by a perfect square except 1. Let p be an odd prime. For n with (n, p) = 1, the smallest positive integer f such that n (f) a parts per thousand 1 (mod p) is called the exponent of n modulo p. If the exponent of n modulo p is p - 1, then n is called a primitive root mod p. Let A(n) be the characteristic function of the square-free primitive roots modulo p. In this paper we study the distribution Sigma(n <= x) A(n)A(n+1), and give an asymptotic formula by using properties of character sums.