On the Arkhipov–Karatsuba Multivariate System
of Congruences
H. M. Salibaa and V. N. Chubarikovb*
Translated by O. Sipacheva
a Notre Dame University, Louaize, Lebanon
b Mechanics and Mathematics Faculty, Moscow State University, Moscow, 119991 Russia
Correspondence to: * e-mail: chubarik2009@live.ru
Received 18 October, 2016
Abstract—The Arkhipov–Karatsuba multivariate system of congruences modulo any prime greater than the degrees of forms in this system is solvable for any right-hand sides and any number of variables larger than $8(n + 1)m{{\log }_{2}}(rn) + 12(n + 1)m + 4(n + 1)$, where $n$ is the degree of the forms in the system and m = $\left( \begin{gathered} n + r - 1 \\ r - 1 \\ \end{gathered} \right)$ is the number of congruences.
DOI: 10.1134/S1064562417010252