On the distribution of modular inverses from short intervals

Abstract

AbstractFor a prime number p and integer x with , let denote the multiplicative inverse of x modulo p. In this paper, we are interested in the problem of distribution modulo p of the sequence and in lower bound estimates for the corresponding exponential sums. As representative examples, we state the following two consequences of the main results.For any fixed and for any sufficiently large integer N, there exists a prime number p with such that For any fixed positive , there exists a positive constant c such that the following holds: for any sufficiently large integer N there is a prime number such that and