Solve (3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)

$$( 3 + 1 ) ( 3 ^ { 2 } + 1 ) ( 3 ^ { 4 } + 1 ) ( 3 ^ { 8 } + 1 ) ( 3 ^ { 16 } + 1 )$$

Evaluate

$$926510094425920$$

Solution Steps

Add 3 and 1 to get 4.

$$4\left(3^{2}+1\right)\left(3^{4}+1\right)\left(3^{8}+1\right)\left(3^{16}+1\right)$$

Calculate 3 to the power of 2 and get 9.

$$4\left(9+1\right)\left(3^{4}+1\right)\left(3^{8}+1\right)\left(3^{16}+1\right)$$

Add 9 and 1 to get 10.

$$4\times 10\left(3^{4}+1\right)\left(3^{8}+1\right)\left(3^{16}+1\right)$$

Multiply 4 and 10 to get 40.

$$40\left(3^{4}+1\right)\left(3^{8}+1\right)\left(3^{16}+1\right)$$

Calculate 3 to the power of 4 and get 81.

$$40\left(81+1\right)\left(3^{8}+1\right)\left(3^{16}+1\right)$$

Add 81 and 1 to get 82.

$$40\times 82\left(3^{8}+1\right)\left(3^{16}+1\right)$$

Multiply 40 and 82 to get 3280.

$$3280\left(3^{8}+1\right)\left(3^{16}+1\right)$$

Calculate 3 to the power of 8 and get 6561.

$$3280\left(6561+1\right)\left(3^{16}+1\right)$$

Add 6561 and 1 to get 6562.

$$3280\times 6562\left(3^{16}+1\right)$$

Multiply 3280 and 6562 to get 21523360.

$$21523360\left(3^{16}+1\right)$$

Calculate 3 to the power of 16 and get 43046721.

$$21523360\left(43046721+1\right)$$

Add 43046721 and 1 to get 43046722.

$$21523360\times 43046722$$

Multiply 21523360 and 43046722 to get 926510094425920.

$$926510094425920$$

Factor

$$2^{6}\times 5\times 17\times 41\times 193\times 21523361$$