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

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

Calcular

$$6004800933418326$$

Pasos de la solución

Calcula 2 a la potencia de 2 y obtiene 4.

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

Suma 4 y 1 para obtener 5.

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

Calcula 2 a la potencia de 4 y obtiene 16.

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

Suma 16 y 1 para obtener 17.

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

Multiplica 5 y 17 para obtener 85.

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

Calcula 2 a la potencia de 8 y obtiene 256.

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

Suma 256 y 1 para obtener 257.

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

Multiplica 85 y 257 para obtener 21845.

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

Calcula 2 a la potencia de 16 y obtiene 65536.

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

Suma 65536 y 1 para obtener 65537.

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

Multiplica 21845 y 65537 para obtener 1431655765.

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

Calcula 2 a la potencia de 22 y obtiene 4194304.

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

Suma 4194304 y 1 para obtener 4194305.

$$1431655765\times 4194305+1$$

Multiplica 1431655765 y 4194305 para obtener 6004800933418325.

$$6004800933418325+1$$

Suma 6004800933418325 y 1 para obtener 6004800933418326.

$$6004800933418326$$

Factorizar

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