Question

12(5²+1)(5⁴+1)(5⁸+1)(5¹⁶+1)

Answer 1

Đặt đa thức \(12\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\) là A:

\(2A=24.\left(5^2+1\right)\left(5^4+1\right)...\left(5^{16}+1\right)\)

\(2A=\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right)...\left(5^{16}+1\right)\)

\(2A=\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\)

\(2A=\left(5^8-1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)

\(2A=\left(5^{16}-1\right)\left(5^{16}+1\right)\)

\(2A=5^{32}-1\)

\(A=\frac{5^{32}-1}{2}\)