Proof of a conjectural supercongruence

Let $m>2$ and $q>0$ be integers with $m$ even or $q$ odd. We show the supercongruence $\sum_{k=0}^{p-1}(-1)^{km}\binom{p/m-q}{k}^m\equiv0\pmod{p^3}.$ for any prime $p>mq$. This confirms a conjecture of Sun.

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