Geodesic
Additive problems with numbers having a given number of prime dividers from progressions
Fundamentalʹnaâ i prikladnaâ matematika, Tome 3 (1997) no. 1, pp. 163-170.

Voir la notice de l'article provenant de la source Math-Net.Ru

We have found the number of the representations of a number $N$ as $$ n=mr\quadand\quad n+m^2+r^2, $$ 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. 
@article{FPM_1997_3_1_a13,
     author = {A. A. Zhukova},
     title = {Additive problems with numbers having a given number of prime dividers from progressions},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {163--170},
     publisher = {mathdoc},
     volume = {3},
     number = {1},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_1997_3_1_a13/}
}
TY  - JOUR
AU  - A. A. Zhukova
TI  - Additive problems with numbers having a given number of prime dividers from progressions
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 1997
SP  - 163
EP  - 170
VL  - 3
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_1997_3_1_a13/
LA  - ru
ID  - FPM_1997_3_1_a13
ER  - 
%0 Journal Article
%A A. A. Zhukova
%T Additive problems with numbers having a given number of prime dividers from progressions
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 1997
%P 163-170
%V 3
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_1997_3_1_a13/
%G ru
%F FPM_1997_3_1_a13
A. A. Zhukova. Additive problems with numbers having a given number of prime dividers from progressions. Fundamentalʹnaâ i prikladnaâ matematika, Tome 3 (1997) no. 1, pp. 163-170. http://geodesic.mathdoc.fr/item/FPM_1997_3_1_a13/