Type: Article

The Congruence x (x) lambda (mod p)

Cilleruelo, J; Garaev, M. Z.;

Abstract:

In the present paper we obtain several new results related to the problem of upper bound estimates for the number of solutions of the congruence x(x) lambda (mod p); x is an element of N, x <= p - 1, where p is a large prime number and lambda is an integer coprime to p. Our arguments are based on recent estimates of trigonometric sums over subgroups due to Shkredov and Shteinikov.