Solve (2^2+1)(2^4+1)(2^8+1)(2^16+1)

$$( 2 ^ { 2 } + 1 ) ( 2 ^ { 4 } + 1 ) ( 2 ^ { 8 } + 1 ) ( 2 ^ { 16 } + 1 )$$

Evaluate

$$1431655765$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$\left(4+1\right)\left(2^{4}+1\right)\left(2^{8}+1\right)\left(2^{16}+1\right)$$

Add 4 and 1 to get 5.

$$5\left(2^{4}+1\right)\left(2^{8}+1\right)\left(2^{16}+1\right)$$

Calculate 2 to the power of 4 and get 16.

$$5\left(16+1\right)\left(2^{8}+1\right)\left(2^{16}+1\right)$$

Add 16 and 1 to get 17.

$$5\times 17\left(2^{8}+1\right)\left(2^{16}+1\right)$$

Multiply 5 and 17 to get 85.

$$85\left(2^{8}+1\right)\left(2^{16}+1\right)$$

Calculate 2 to the power of 8 and get 256.

$$85\left(256+1\right)\left(2^{16}+1\right)$$

Add 256 and 1 to get 257.

$$85\times 257\left(2^{16}+1\right)$$

Multiply 85 and 257 to get 21845.

$$21845\left(2^{16}+1\right)$$

Calculate 2 to the power of 16 and get 65536.

$$21845\left(65536+1\right)$$

Add 65536 and 1 to get 65537.

$$21845\times 65537$$

Multiply 21845 and 65537 to get 1431655765.

$$1431655765$$

Factor

$$5\times 17\times 257\times 65537$$