Solve 6(7+1)(7^2+1)(7^4+1)(7^8+1)(7^16+1)+1=

$$6 ( 7 + 1 ) ( 7 ^ { 2 } + 1 ) ( 7 ^ { 4 } + 1 ) ( 7 ^ { 8 } + 1 ) ( 7 ^ { 16 } + 1 ) + 1 =$$

Evaluate

$$1104427674243920646305299201$$

Solution Steps

Add 7 and 1 to get 8.

$$6\times 8\left(7^{2}+1\right)\left(7^{4}+1\right)\left(7^{8}+1\right)\left(7^{16}+1\right)+1$$

Multiply 6 and 8 to get 48.

$$48\left(7^{2}+1\right)\left(7^{4}+1\right)\left(7^{8}+1\right)\left(7^{16}+1\right)+1$$

Calculate 7 to the power of 2 and get 49.

$$48\left(49+1\right)\left(7^{4}+1\right)\left(7^{8}+1\right)\left(7^{16}+1\right)+1$$

Add 49 and 1 to get 50.

$$48\times 50\left(7^{4}+1\right)\left(7^{8}+1\right)\left(7^{16}+1\right)+1$$

Multiply 48 and 50 to get 2400.

$$2400\left(7^{4}+1\right)\left(7^{8}+1\right)\left(7^{16}+1\right)+1$$

Calculate 7 to the power of 4 and get 2401.

$$2400\left(2401+1\right)\left(7^{8}+1\right)\left(7^{16}+1\right)+1$$

Add 2401 and 1 to get 2402.

$$2400\times 2402\left(7^{8}+1\right)\left(7^{16}+1\right)+1$$

Multiply 2400 and 2402 to get 5764800.

$$5764800\left(7^{8}+1\right)\left(7^{16}+1\right)+1$$

Calculate 7 to the power of 8 and get 5764801.

$$5764800\left(5764801+1\right)\left(7^{16}+1\right)+1$$

Add 5764801 and 1 to get 5764802.

$$5764800\times 5764802\left(7^{16}+1\right)+1$$

Multiply 5764800 and 5764802 to get 33232930569600.

$$33232930569600\left(7^{16}+1\right)+1$$

Calculate 7 to the power of 16 and get 33232930569601.

$$33232930569600\left(33232930569601+1\right)+1$$

Add 33232930569601 and 1 to get 33232930569602.

$$33232930569600\times 33232930569602+1$$

Multiply 33232930569600 and 33232930569602 to get 1104427674243920646305299200.

$$1104427674243920646305299200+1$$

Add 1104427674243920646305299200 and 1 to get 1104427674243920646305299201.

$$1104427674243920646305299201$$

Factor

$$7^{32}$$