Question Number 146072 by savitar last updated on 10/Jul/21
![Let F_n =2^2^n +1 the fermat number Prove that F_n is prime ⇔ 3^((F_n −1)/2) ≡1[F_n ]](https://www.tinkutara.com/question/Q146072.png)
$${Let}\:{F}_{{n}} =\mathrm{2}^{\mathrm{2}^{{n}} } +\mathrm{1}\:{the}\:{fermat}\:{number} \\ $$$${Prove}\:{that} \\ $$$$\:{F}_{{n}} \:{is}\:{prime}\:\Leftrightarrow\:\mathrm{3}^{\frac{{F}_{{n}} −\mathrm{1}}{\mathrm{2}}} \equiv\mathrm{1}\left[{F}_{{n}} \right] \\ $$