Let $S_{3}(x)$ denote the number of positive integers not exceeding x which can be expressed as a sum of three squares. Can we find an asymptotic formula for $S_{3}(x)$, maybe using Landau-Ramanujan theorem?

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    $\begingroup$ www.ams.org/tran/1951-071-01/S0002-9947-1951-0042438-4 $\endgroup$ – Jack D'Aurizio Jan 29 '16 at 9:21
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    $\begingroup$ Every positive integer can be expressed as a sum of three squares except those of the form $4^n(8m+7)$, so $S_3(x)=(5/6)x+O(1)$. $\endgroup$ – Gerry Myerson Jan 29 '16 at 9:54

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