A question of divisibility. (NBHM 2012) The number $18! + 1$ is divisible by 437. How to prove it?  I have $(19-1)! + 1 \equiv 0$ (mod 19) and $437 = 19 \times 23$. What to do next?  Thank you for your help.
how to prove $437\,$ divides $18!+1$? (NBHM 2012) I was solving some problems and I came across this problem. I didn't understand how to approach this problem. Can we solve this with out actually calculating $18!\,\,?$
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