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On a symmetric congruence and its applications

M. Z. Garaev·A. A. Karatsuba
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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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M. Z. Garaev, A. A. Karatsuba. 2005-03-16. On a symmetric congruence and its applications. https://arxiv.org/abs/math/0503164

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