Let Sn=∑k=1nk⋅k!S_n = \sum_{k=1}^n k \cdot k!Sn=∑k=1nk⋅k!. For which prime numbers ppp does ppp divide Sp−1S_{p-1}Sp−1?
No prime ppp
All primes ppp
All primes p>3p > 3p>3
Only p=2p = 2p=2