Lựa chọn đáp án đúng nhất: So sánh A = (2 + 1)(2^2 + 1)(2^4 + 1

* Hướng dẫn giải

Đáp án C

Ta có:

$$\begin{gathered} A=\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right) \\ =1.\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right) \\ =\left(2-1\right)\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right) \\ =\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right) \\ =\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right) \\ =(2^8-1)(2^8+1)(2^{16}+1) \\ =(2^{16}-1)(2^{16}+1)\text{}=2^{32}-1 \end{gathered}$$

Do đó A = B

Vậy đáp án là C