I want to find $n$ so that $\frac{n!-1}{3n+1}$ is an integer. Assume that $3n+1$ is prime (there are only finitely many solutions where $3n+1$ is composite).
2026-05-16 02:36:50.1778899010
Determine when $\frac{n!-1}{3n+1}$ is an integer
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