(2+1)(2²+1)(2四次方+1)……(2n次方+1)
=(2-1)(2+1)(2²+1)(2四次方+1)……(2n次方+1)
=(2²-1)(2²+1)(2四次方+1)……(2n次方+1)
=(2四次方-1)(2四次方+1)……(2n次方+1)
=(2八次方-1)……(2n次方+1)
.
=(2n次方-1)(2n次方+1)
=2的2n次方-1
(2+1)(2²+1)(2四次方+1)……(2n次方+1)
=(2-1)(2+1)(2²+1)(2四次方+1)……(2n次方+1)
=(2²-1)(2²+1)(2四次方+1)……(2n次方+1)
=(2四次方-1)(2四次方+1)……(2n次方+1)
=(2八次方-1)……(2n次方+1)
.
=(2n次方-1)(2n次方+1)
=2的2n次方-1