Resolver (2^{2}+1)(2^4+1)(2^8+1)(2^16+1)(2^22+1)+1

$$( 2 ^ { 2 } + 1 ) ( 2 ^ { 4 } + 1 ) ( 2 ^ { 8 } + 1 ) ( 2 ^ { 16 } + 1 ) ( 2 ^ { 22 } + 1 ) + 1$$

Avaliar

$$6004800933418326$$

Passos Para a Resolução

Calcule 2 elevado a 2 e obtenha 4.

$$\left(4+1\right)\left(2^{4}+1\right)\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{22}+1\right)+1$$

Some 4 e 1 para obter 5.

$$5\left(2^{4}+1\right)\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{22}+1\right)+1$$

Calcule 2 elevado a 4 e obtenha 16.

$$5\left(16+1\right)\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{22}+1\right)+1$$

Some 16 e 1 para obter 17.

$$5\times 17\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{22}+1\right)+1$$

Multiplique 5 e 17 para obter 85.

$$85\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{22}+1\right)+1$$

Calcule 2 elevado a 8 e obtenha 256.

$$85\left(256+1\right)\left(2^{16}+1\right)\left(2^{22}+1\right)+1$$

Some 256 e 1 para obter 257.

$$85\times 257\left(2^{16}+1\right)\left(2^{22}+1\right)+1$$

Multiplique 85 e 257 para obter 21845.

$$21845\left(2^{16}+1\right)\left(2^{22}+1\right)+1$$

Calcule 2 elevado a 16 e obtenha 65536.

$$21845\left(65536+1\right)\left(2^{22}+1\right)+1$$

Some 65536 e 1 para obter 65537.

$$21845\times 65537\left(2^{22}+1\right)+1$$

Multiplique 21845 e 65537 para obter 1431655765.

$$1431655765\left(2^{22}+1\right)+1$$

Calcule 2 elevado a 22 e obtenha 4194304.

$$1431655765\left(4194304+1\right)+1$$

Some 4194304 e 1 para obter 4194305.

$$1431655765\times 4194305+1$$

Multiplique 1431655765 e 4194305 para obter 6004800933418325.

$$6004800933418325+1$$

Some 6004800933418325 e 1 para obter 6004800933418326.

$$6004800933418326$$

Fatorizar

$$2\times 3\times 13\times 683\times 3881\times 29042879$$