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(1986)
An estimate of the number of summands in the Hubert—Kamke problem
A. Karatsuba (1976)
A system of congruencesMathematical notes of the Academy of Sciences of the USSR, 19
(1986)
Chubarikov, On simultaneous representation of positive integers as sums of powers of prime numbers
(1986)
On the singular series in the Hilbert-Kamke problem
(1984)
On the Hubert-Kamke problem
(1952)
On the number of solutions of Tarr/s problem
D Mit'kin (1987)
On the Hilbert-Kamke problem in prime numbersRussian Mathematical Surveys, 42
(1950)
Additive Primzahltheone
-- In this paper it is proved that the number of summands , which are required for the simultaneous representations of positive integers Njf1<j< n, satisfying the corresponding necessary arithmetic conditions, as sums of the jth powers of prime numbers «,· > + 1, 1 < i < , belongs to some residue class modulo Ro(n) = exp{n In + O(n)}, moreover, if > 17, then for every class of numbers Ni,...,Nn, corresponding to s modulo Ao(n), the least , which is sufficient for these representations, is determined from the inequalities 80(n) < a < sQ(n) + Ro(n) - 1, where 80(n) ~ 3an, an ~ 3n/4, --> oo, provided that the numbers NI , . . . , Nn satisfy some order conditions and are large enough. The analogous situation has arisen for simultaneous representations of NI , . . . , Nn as sums of powers of arbitrary prime numbers. 1. INTRODUCTION Let > 2, 5, NI,... , Nn be positive integers, and let J be the number of solutions of the system of equations * + ... + * = ^, j = l,...,n, (1) in prime numbers, and = N^n. For fixed > 11,
Discrete Mathematics and Applications – de Gruyter
Published: Jan 1, 1993
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