$(2 + 1)(2^2 + 1)(2^4 + 1)(2^8 + 1)(2^{16} + 1)(2^{32} + 1) = (2 - 1)(2 + 1)(2^2 + 1)(2^4 + 1)(2^8 + 1)(2^{16} + 1)(2^{32} + 1) = (2^2 - 1)(2^2 + 1)(2^4 + 1)(2^8 + 1)(2^{16} + 1)(2^{32} + 1) = (2^4 - 1)(2^4 + 1)(2^8 + 1)(2^{16} + 1)(2^{32} + 1) = (2^8 - 1)(2^8 + 1)(2^{16} + 1)(2^{32} + 1) = (2^{16} - 1)(2^{16} + 1)(2^{32} + 1) = (2^{32} - 1)(2^{32} + 1) = 2^{64} - 1$

$\frac{(2 + 1)(2^2 + 1)(2^4 + 1)(2^8 + 1)(2^{16} + 1)(2^{32} + 1) + 1}{2^{64}} = \frac{(2 - 1)(2 + 1)(2^2 + 1)(2^4 + 1)(2^8 + 1)(2^{16} + 1)(2^{32} + 1) + 1}{2^{64}} = \frac{(2^2 - 1)(2^2 + 1)(2^4 + 1)(2^8 + 1)(2^{16} + 1)(2^{32} + 1) + 1}{2^{64}} = \frac{(2^4 - 1)(2^4 + 1)(2^8 + 1)(2^{16} + 1)(2^{32} + 1) + 1}{2^{64}} = \frac{(2^8 - 1)(2^8 + 1)(2^{16} + 1)(2^{32} + 1) + 1}{2^{64}} = \frac{(2^{16} - 1)(2^{16} + 1)(2^{32} + 1) + 1}{2^{64}} = \frac{(2^{32} - 1)(2^{32} + 1) + 1}{2^{64}} = \frac{2^{64} - 1 + 1}{2^{64}} = \frac{2^{64}}{2^{64}} = 1$

$\frac{(3 + 2)(3^2 + 2^2)(3^4 + 2^4)(3^8 + 2^8)(3^{16} + 2^{16})(3^{32} + 2^{32}) + 2^{64}}{3^{64}} = \frac{(3 - 2)(3 + 2)(3^2 + 2^2)(3^4 + 2^4)(3^8 + 2^8)(3^{16} + 2^{16})(3^{32} + 2^{32}) + 2^{64}}{3^{64}} = \frac{(3^2 - 2^2)(3^2 + 2^2)(3^4 + 2^4)(3^8 + 2^8)(3^{16} + 2^{16})(3^{32} + 2^{32}) + 2^{64}}{3^{64}} = \frac{(3^4 - 2^4)(3^4 + 2^4)(3^8 + 2^8)(3^{16} + 2^{16})(3^{32} + 2^{32}) + 2^{64}}{3^{64}} = \frac{(3^8 - 2^8)(3^8 + 2^8)(3^{16} + 2^{16})(3^{32} + 2^{32}) + 2^{64}}{3^{64}} = \frac{(3^{16} - 2^{16})(3^{16} + 2^{16})(3^{32} + 2^{32}) + 2^{64}}{3^{64}} = \frac{(3^{32} - 2^{32})(3^{32} + 2^{32}) + 2^{64}}{3^{64}} = \frac{3^{64} - 2^{64} + 2^{64}}{3^{64}} = \frac{3^{64}}{3^{64}} = 1$