Half Factorial

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Prove : For any positive integers p, k,
(p^k)!  \text { is divisible by p }
Proof:
Apply Factorial Formula:
\boxed {n!=n.(n-1)! }

(p^k)! = (p^k). (p^k -1)!  = p.(p^{k-1}).(p^k -1)!
hence divisible by p. [QED]

See also:
Why 0!=1

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