Question Number 29036 by abdo imad last updated on 03/Feb/18
![p=2m+1 is a prime number prove that 1) (p−1)!≡ −1[p] 2) (m!)^2 ≡ (−1)^(m+1) [p]](Q29036.png)
$${p}=\mathrm{2}{m}+\mathrm{1}\:{is}\:{a}\:{prime}\:{number}\:{prove}\:{that} \\ $$$$\left.\mathrm{1}\right)\:\left({p}−\mathrm{1}\right)!\equiv\:−\mathrm{1}\left[{p}\right] \\ $$$$\left.\mathrm{2}\right)\:\left({m}!\right)^{\mathrm{2}} \equiv\:\left(−\mathrm{1}\right)^{{m}+\mathrm{1}} \:\left[{p}\right] \\ $$