The distribution of Hardy–Littlewood numbers in arithmetic progressions

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.
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