On extreme values of $r_3(n)$ in arithmetic progressions

Michael Filaseta, Jonah Klein, Cihan Sabuncu

For a given integer $m$ and any residue $a(\mathrm{mod}m)$ that can be written as a sum of 3 squares modulo $m$, we show the existence of infinitely many integers $n\equiv a(\mathrm{mod}m)$ s…