Twelve Factorial plus One is divisible by 13 Squared

Theorem

$12! + 1$ is divisible by $13^2$.

Proof

By calculuation:

\(\ds 12! + 1\)

\(=\)

\(\ds 479 \, 001 \, 601\)

\(\ds \)

\(=\)

\(\ds 2 \, 834 \, 329 \times 13 \times 13\)

$\blacksquare$

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $13$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $13$