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Does $$p \mid 1! + 2! + 3! + 4! + \cdots + (p-1)!$$ ever occur for any prime $p$?

My friend told me about this problem, but I don't know the source.

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up vote 7 down vote accepted

It happens when $p=3$, but fails when $p=2$, so it only works for some primes.

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Thank you. I had overlooked p=3 which is embarassing.. and my computer program was wrong - I fixed it now and asked an updated questio. math.stackexchange.com/questions/337053/… – user58512 Mar 21 '13 at 17:08

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