FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
1997, VOLUME 3, NUMBER 1, PAGES 163-170
A. A. Zhukova
Abstract
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We have found the number of the representations of a number $N$ as
$$
n=mr\quad \mbox{and}\quad n+m^2+r^2,
$$
where $m,r$ --- natural numbers and $n$ are the numbers having
$k$ prime dividers such that
$p_i\equiv l_i\, (\bmod\ d_0)$ ,
$p_i\geq t> \ln^{B+1}N$ , $(l_i,d_0)=1$ , $i=1,2,\ldots,k$ ,
$(N-l_1\ldots l_k,d_0)=1$ .
The paper also contains the results about distribution of
such numbers $n$
in arithmetic progressions with large modulus.
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