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asymptotic formulae

Proceedings of the Edinburgh Mathematical Society (1)

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THE REPRESENTATION OF RESIDUE CLASSES BY PRODUCTS OF SMALL INTEGERS
M. Z. Garaev, A. A. Karatsuba
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 50 / Issue 2 / June 2007

Published online by Cambridge University Press:

17 May 2007, pp. 363-375
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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 $m$.