I want to prove the statement "Any prime factor of $x!+1$ is larger than $x$."
Any slight hint will be ok.
2026-04-04 17:13:10.1775322790
Prove that any prime factor of $ ( x!+1)$ is larger than$ x$.
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Assume $p \leq x$ divides $x! + 1$. Then, $p$ also divides $x!$ (as any $y \leq x$ divides $x!$). Thus, $p$ divides both $x!$ and $x! + 1$. Do you see what this forces $p$ to be?