Originally Posted by

**undefined** You missed a carat symbol, and I initially got an incorrect result based on your definition (didn't take long though). It should be

$\displaystyle F_m=2^{2^m}+1$

This part is easy to derive

$\displaystyle F_{m+1}=2^{2^{m+1}}+1 = 2^{2 \cdot 2^m}+1$

$\displaystyle =\left(2^{2^m}\right)^2+1$

$\displaystyle =(F_m-1)^2+1$

Haven't worked on the rest of the problem.. I won't have time today, so I'm guessing by the time I would be able to work on everything else, someone will already have addressed it.