On a symmetric congruence and its applications

M. Z. Garaev, A. A. Karatsuba

Published 2005-03-08, updated 2005-03-16Version 2

For a large integer $m,$ we obtain an asymptotic formula for the number of solutions of a certain congruence modulo $m$ with four variables, where the variables belong to special sets of residue classes modulo $m.$ This formula are applied to obtain new information on the exceptional set of the multiplication table problem in a residue ring modulo $m$ and a new bound for a double trigonometric sum with an exponential function.