证明2^32+1不是质数

设:$a=2^7$,$b=5$
$\therefore a-b^3=3$
$\therefore b(a-b^3)+1=16=2^4$
$$\begin{array}{rl}\therefore 2^{32}+1& =2^4\ast 2^{28}+1\\ & =\left[b\ast (a-b^3)+1\right]\ast a^4+1\\ & =(ab-b^4)\ast a^4+a^4+1\\ & =(1-a^4\ast b^4)+a^4\ast (1+ab)\\ & =(1+a^2{b}^2)(1+ab)(1-ab)+a^4\ast (1+ab)\\ & =(1+ab)\ast \left[(1+a^2{b}^2)(1-ab)+a^4\right]\end{array}$$
$\therefore 2^{32}+1$不是质数