Rút gọn biểu thức: \(P = 12\left( {{5^2} + 1} \right)\left( {{5^4} + 1} \right)\left( {{5^8} + 1} \right)\left( {{5^{16}} + 1} \right)\)
\(P = 12\left( {{5^2} + 1} \right)\left( {{5^4} + 1} \right)\left( {{5^8} + 1} \right)\left( {{5^{16}} + 1} \right)\)
\(\eqalign{ & = {1 \over 2}\left( {{5^2} – 1} \right)\left( {{5^2} + 1} \right)\left( {{5^4} + 1} \right)\left( {{5^4} + 1} \right)\left( {{5^8} + 1} \right)\left( {{5^{16}} + 1} \right) \cr & = {1 \over 2}\left( {{5^4} – 1} \right)\left( {{5^4} + 1} \right)\left( {{5^8} + 1} \right)\left( {{5^{16}} + 1} \right) \cr & = {1 \over 2}\left( {{5^8} – 1} \right)\left( {{5^8} + 1} \right)\left( {{5^{16}} + 1} \right) \cr & = {1 \over 2}\left( {{5^{16}} – 1} \right)\left( {{5^{16}} + 1} \right) = {1 \over 2}\left( {{5^{32}} – 1} \right) \cr} \)