NO-ABEL 1993 Problem 3

The Fermat-numbers are defined by $F_n = 2^{2^n}+1$ for $n\in N$ . (a) Prove that $F_n = F_{n-1}F_{n-2}....F_1F_0 +2$ for $n > 0$ . (b) Prove that any two different Fermat numbers are coprime