1) Show that ifnis a positive integer andaandbare integers relatively prime tonsuch that $\displaystyle (ord_{n}a, ord_{n}b)$ = 1, then $\displaystyle ord_{n}(ab)$ = $\displaystyle ord_{n}a * ord_{n}b$

2) Letpbe a prime divisor of the Fermat number $\displaystyle F_{n} = 2^{2n} + 1$

a) Show that $\displaystyle ord_{p}2 = 2^n + 1$

b) From part (a), conclude that $\displaystyle 2^{n+1} \mid (p-1)$, so thatpmust be of the form $\displaystyle 2^{n+1}k + 1$