I am studying Wilson's Theorem where the previous corollary came up to my mind. Is it a true one? If so, this might be a generalized version of the Theorem.
2026-03-26 17:37:33.1774546653
$\Pi_{i=1}^{p-1}(i-1)kp + i \equiv -1 \pmod p, k \in \mathbb{Z}$ where $p$ is a prime
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Once you reduce all parts of the product on the left $\textrm{mod}\,p$ (now that you have edited the question), this says $\left(p-1\right)! \equiv -1 \left(\textrm{mod}\, p\right)$, so I'd say so.