Chapter 0.2, Problem 35E

(a)

To determine

$2^{4n+2}+1$($n$ a positive integer) and $2^{18}+1$ as the product of two integers each greater than 1 by using the identity $4x^4+1=\left(2x^2+2x+1\right)\left(2x^2-2x+1\right)$ where $x$ is any real number.

(b)

To determine

$2^{36}-1$ as the product of four integers each of which is larger than 1 by using the identity $4x^4+1=\left(2x^2+2x+1\right)\left(2x^2-2x+1\right)$ where $x$ is any real number.