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THE REPRESENTATION OF RESIDUE CLASSES BY PRODUCTS OF SMALL INTEGERS

Published online by Cambridge University Press:  17 May 2007

M. Z. Garaev  and
A. A. Karatsuba
M. Z. Garaev
Affiliation:
Instituto de Matemáticas, Universidad Nacional Autónoma de México, Campus Morelia, Apartado Postal 61-3 (Xangari), CP 58089, Morelia, Michoacán, Mexico (garaev@matmor.unam.mx)
A. A. Karatsuba
Affiliation:
Steklov Institute of Mathematics, Russian Academy of Sciences, GSP-1, ul. Gubkina 8, Moscow, Russiakaratsuba@mi.ras.ru
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Abstract

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For a large integer $m$, we obtain asymptotic formulae for the number of solutions of certain congruences modulo $m$ with several variables, where the variables belong to special sets of residue classes modulo $m$. In particular, we obtain new information on the exceptional set of the multiplication table problem in the residue ring modulo $m$.

Keywords

Primary 11A0711B5011L07congruencestrigonometric sumsnumber of solutionsasymptotic formulae
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 50 , Issue 2 , June 2007 , pp. 363 - 375
Copyright
Copyright © Edinburgh Mathematical Society 2007