Exercise 15, § 1

A number of the form $2^k + 1$ ($k \geq 1$ an integer) can be a prime only if k is a power of 2. If a prime number p divides $2^{2^n} + 1$, then it cannot divide $2^{2^m} + 1$ for $m > n$ ($2^{2^m} \equiv 1(p)$); use this to give a new proof of Prop. 5. Show that $2^{2^5} + 1$ is not prime (put $a = 2^7$ and $b = 5$; show that $1 + ab - b^4 = 2^4$ and that $1 + ab$ divides