Sign up ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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.

share|cite|improve this question

1 Answer 1

up vote 7 down vote accepted

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

share|cite|improve this answer
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.… – user58512 Mar 21 '13 at 17:08

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.