On a symmetric congruence and its applications
Abstract
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.
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