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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It happens when $p=3$, but fails when $p=2$, so it only works for some primes.
Cameron Buie
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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. http://math.stackexchange.com/questions/337053/second-part-of-the-factorial-sum-divisibility-question – Mar 21 '13 at 17:08