  Let the numbers $\alpha_n,\beta_n$ and $\gamma_n$ denote \begin{align*}
\alpha_n=\sum_{k=0}^{n-1}{2k\choose k},\quad \beta_n=\sum_{k=0}^{n-1}{2k\choose
k}\frac{1}{k+1}\quad\text{and}\quad \gamma_n=\sum_{k=0}^{n-1}{2k\choose
k}\frac{3k+2}{k+1}, \end{align*} respectively. We prove that for any prime
$p\ge 5$ and positive integer $n$ \begin{align*} \alpha_{np}&\equiv
\left(\frac{p}{3}\right) \alpha_n \pmod{p^2},\\ \beta_{np}&\equiv \begin{cases}
\displaystyle \beta_n \pmod{p^2},\quad &\text{if $p\equiv 1\pmod{3}$},\\
-\gamma_n \pmod{p^2},\quad &\text{if $p\equiv 2\pmod{3}$}, \end{cases}
\end{align*} where $\left(\frac{\cdot}{p}\right)$ denotes the Legendre symbol.
These two supercongruences were recently conjectured by Apagodu and Zeilberger.
