M@X -- Math At Xavier Mathematics Department Xavier University of Louisiana
	Fall 2022 seminar Spring 2023 seminar
	\begin{eqnarray*} \sum_{k=0}^{(p-1)/2}\frac{\binom{2k}{k} \binom{3k}{k}}{27^k}&\equiv & \left(\frac{p}{3}\right)\frac{2^p+1}{3} \pmod{p^2} \\[2ex] \sum_{k=0}^{(p-1)/2}\frac{\binom{6k}{3k} \binom{3k}{k}}{(2k+1)432^k}&\equiv & \left(\frac{p}{3}\right)\frac{3^p+1}{4} \pmod{p^2} \\[2ex] \sum_{k=0}^{(p-1)/2}\frac{\binom{4k}{2k} \binom{2k}{k}}{(2k+1)64^k}&\equiv & \left(\frac{-1}{3}\right)2^{p-1} \pmod{p^2} \end{eqnarray*}