\[\boxed{\text{1229.}\text{\ }еуроки - ответы\ на\ пятёрку}\]
\[Умножим\ выражение\ на\ 1 =\]
\[= (2 - 1):\]
\[(2 - 1)(2 + 1)\left( 2^{2} + 1 \right)\left( 2^{4} + 1 \right)\]
\[\left( 2^{8} + 1 \right)\left( 2^{16} + 1 \right)\left( 2^{32} + 1 \right) =\]
\[= \left( 2^{2} - 1 \right)\left( 2^{2} + 1 \right)\left( 2^{4} + 1 \right)\]
\[\left( 2^{8} + 1 \right)\left( 2^{16} + 1 \right)\left( 2^{32} + 1 \right) =\]
\[= \left( 2^{4} - 1 \right)\left( 2^{4} + 1 \right)\left( 2^{8} + 1 \right)\]
\[\left( 2^{16} + 1 \right)\left( 2^{32} + 1 \right) =\]
\[= \left( 2^{8} - 1 \right)\left( 2^{8} + 1 \right)\left( 2^{16} + 1 \right)\]
\[\left( 2^{32} + 1 \right) = \left( 2^{16} - 1 \right)\]
\[\left( 2^{16} + 1 \right)\left( 2^{32} + 1 \right) =\]
\[= \left( 2^{32} - 1 \right)\left( 2^{32} + 1 \right) = 2^{64} - 1\]