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

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

Calcular

$$21474836476$$

Pasos de la solución

Multiplica 2^{2}+1 y 2^{2}+1 para obtener \left(2^{2}+1\right)^{2}.

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

Suma 2 y 1 para obtener 3.

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

Calcula 2 a la potencia de 2 y obtiene 4.

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

Suma 4 y 1 para obtener 5.

$$3\times 5^{2}\left(2^{4}+1\right)\left(2^{8}+1\right)\left(2^{16}+1\right)+1$$

Calcula 5 a la potencia de 2 y obtiene 25.

$$3\times 25\left(2^{4}+1\right)\left(2^{8}+1\right)\left(2^{16}+1\right)+1$$

Multiplica 3 y 25 para obtener 75.

$$75\left(2^{4}+1\right)\left(2^{8}+1\right)\left(2^{16}+1\right)+1$$

Calcula 2 a la potencia de 4 y obtiene 16.

$$75\left(16+1\right)\left(2^{8}+1\right)\left(2^{16}+1\right)+1$$

Suma 16 y 1 para obtener 17.

$$75\times 17\left(2^{8}+1\right)\left(2^{16}+1\right)+1$$

Multiplica 75 y 17 para obtener 1275.

$$1275\left(2^{8}+1\right)\left(2^{16}+1\right)+1$$

Calcula 2 a la potencia de 8 y obtiene 256.

$$1275\left(256+1\right)\left(2^{16}+1\right)+1$$

Suma 256 y 1 para obtener 257.

$$1275\times 257\left(2^{16}+1\right)+1$$

Multiplica 1275 y 257 para obtener 327675.

$$327675\left(2^{16}+1\right)+1$$

Calcula 2 a la potencia de 16 y obtiene 65536.

$$327675\left(65536+1\right)+1$$

Suma 65536 y 1 para obtener 65537.

$$327675\times 65537+1$$

Multiplica 327675 y 65537 para obtener 21474836475.

$$21474836475+1$$

Suma 21474836475 y 1 para obtener 21474836476.

$$21474836476$$

Factorizar

$$2^{2}\times 479\times 11208161$$