Solve left(2+1right)left(2^2+1right)left(2^4+1right)left(2^8+1right)+1

$$\left( 2+1 \right) \left( { 2 }^{ 2 } +1 \right) \left( { 2 }^{ 4 } +1 \right) \left( { 2 }^{ 8 } +1 \right) +1$$

Evaluate

$$65536$$

Solution Steps

Add 2 and 1 to get 3.

$$3\left(2^{2}+1\right)\left(2^{4}+1\right)\left(2^{8}+1\right)+1$$

Calculate 2 to the power of 2 and get 4.

$$3\left(4+1\right)\left(2^{4}+1\right)\left(2^{8}+1\right)+1$$

Add 4 and 1 to get 5.

$$3\times 5\left(2^{4}+1\right)\left(2^{8}+1\right)+1$$

Multiply 3 and 5 to get 15.

$$15\left(2^{4}+1\right)\left(2^{8}+1\right)+1$$

Calculate 2 to the power of 4 and get 16.

$$15\left(16+1\right)\left(2^{8}+1\right)+1$$

Add 16 and 1 to get 17.

$$15\times 17\left(2^{8}+1\right)+1$$

Multiply 15 and 17 to get 255.

$$255\left(2^{8}+1\right)+1$$

Calculate 2 to the power of 8 and get 256.

$$255\left(256+1\right)+1$$

Add 256 and 1 to get 257.

$$255\times 257+1$$

Multiply 255 and 257 to get 65535.

$$65535+1$$

Add 65535 and 1 to get 65536.

$$65536$$

Factor

$$2^{16}$$