Factorial Function (Problem 1)
Level
pending
Inspired by UKMT SMC 2006 Q12:
Prove that always is equivalent to a prime, a multiple of 2 or a multiple of 3.
No
Yes
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1 solution
If you calculate n ! , from 5 ! onwards, it's a multiple of 2 and in some cases 3 . Therefore, n ! + 2 is always either a prime, a multiple of 2 or multiple of 3 . Therefore, the answer is Yes.