Abstract
For positive integers $n$, let $r(n) = \#\{(x,y,z) \in\mathbf{Z}^{3}: x^{2}+y^{2}+z^{2}=n\}$. Let $g$ be a positive integer, and let $A\bmod{M}$ be any congruence class containing a squarefree integer. We show that there are infinitely many squarefree positive integers $n\equiv A\bmod{M}$ for which $g$ divides $r(n)$. This generalizes a result of Cho.
Citation
Paul Pollack. "The representation function for sums of three squares along arithmetic progressions." Proc. Japan Acad. Ser. A Math. Sci. 92 (8) 96 - 99, October 2016. https://doi.org/10.3792/pjaa.92.96
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