Find the Remainder when $100!$ is divided by $97^2$? Find the Remainder when $100!$ is divided by $97^2$?
MyApproach
I applied Wilson Theorem here 
$100$.$99$.$98$.$97$.$96!\text{ mod }97^2=100$.$99$.$98$.$96!\text{ mod }97=-970200$
I am getting wrong Ans
Can Anyone guide me how to approach the problem?

Facts:


*

*$97\text{ is prime}$

*$P\text{ is prime}\iff(P-1)!+1\equiv0\pmod{P}$

*The remainder of $100!$ divided by $97^2$ is equivalent to $\frac{100!}{97}\bmod{97}$



Hence: $96!+1\equiv0\pmod{97}$
Hence: $96!\equiv-1\pmod{97}$
Hence: $96!\equiv96\pmod{97}$
Hence: $\frac{100!}{97}\equiv96!\cdot98\cdot99\cdot100\equiv96\cdot98\cdot99\cdot100\equiv93139200\equiv91\pmod{97}$
