Geodesic
The distribution of Hardy–Littlewood numbers in arithmetic progressions
Izvestiya. Mathematics, Tome 34 (1990) no. 1, pp. 213-228 
Z. Kh. Rakhmonov. The distribution of Hardy–Littlewood numbers in arithmetic progressions. Izvestiya. Mathematics, Tome 34 (1990) no. 1, pp. 213-228. http://geodesic.mathdoc.fr/item/IM2_1990_34_1_a9/
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     title = {The distribution of {Hardy{\textendash}Littlewood} numbers in arithmetic progressions},
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     volume = {34},
     number = {1},
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     url = {http://geodesic.mathdoc.fr/item/IM2_1990_34_1_a9/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

An asymptotic formula is obtained for the number of solutions of the congruence $$ p+n^2\equiv l\ (\operatorname{mod}D),\qquad p\leqslant x,\quad n\leqslant\sqrt x,\quad(l,D)=1, $$ where $D$ is a sufficiently large prime. Bibliography: 7 titles.

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