Geodesic
The number of integers representable as a~sum of two squares on small intervals
Izvestiya. Mathematics , Tome 28 (1987) no. 1, pp. 67-78.

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Let $M(m,h)$ denote the number of natural numbers in the interval $(m;m+h)$ which are representable as a sum of two squares. Under the condition $n>\ln^{42,5+\varepsilon}X$, $\varepsilon>0$, a best possible lower bound for $M(m,h)$ is established for almost all $m\leqslant X$ (for all but $o(X)$). Bibliography: 14 titles. 
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V. A. Plaksin. The number of integers representable as a~sum of two squares on small intervals. Izvestiya. Mathematics , Tome 28 (1987) no. 1, pp. 67-78. http://geodesic.mathdoc.fr/item/IM2_1987_28_1_a3/

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