1) Show that a prime divisorpof the Fermat number $\displaystyle F_{n} = 2^{2^n} + 1$ must be of the form $\displaystyle 2^{n+2}k + 1$.

(Hint: Show that $\displaystyle ord_{p}2 = 2 ^{n+1}$. Then show that $\displaystyle 2^{(p-1)/2}$ is congruent to 1 (mod p). Conclude that $\displaystyle 2^{n+1} \mid$ (p-1)/2)