  Recently, Z.-W. Sun made the following conjecture: for any odd prime $p$ and
odd integer $m$, $$ \frac{1}{m^2{m-1\choose
(m-1)/2}}\Bigg(\sum_{k=0}^{(pm-1)/2}\frac{{2k\choose k}}{8^k}
-\left(\frac{2}{p}\right)\sum_{k=0}^{(m-1)/2}\frac{{2k\choose k}}{8^k}\Bigg)
\equiv 0\pmod{p^2}. $$ In this note, applying the "creative microscoping"
method, introduced by the author and Zudilin, we confirm the above conjecture
of Sun.
