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

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

Avaliar

$$21474836476$$

Passos Para a Resolução

Multiplique 2^{2}+1 e 2^{2}+1 para obter \left(2^{2}+1\right)^{2}.

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

Some 2 e 1 para obter 3.

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

Calcule 2 elevado a 2 e obtenha 4.

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

Some 4 e 1 para obter 5.

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

Calcule 5 elevado a 2 e obtenha 25.

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

Multiplique 3 e 25 para obter 75.

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

Calcule 2 elevado a 4 e obtenha 16.

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

Some 16 e 1 para obter 17.

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

Multiplique 75 e 17 para obter 1275.

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

Calcule 2 elevado a 8 e obtenha 256.

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

Some 256 e 1 para obter 257.

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

Multiplique 1275 e 257 para obter 327675.

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

Calcule 2 elevado a 16 e obtenha 65536.

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

Some 65536 e 1 para obter 65537.

$$327675\times 65537+1$$

Multiplique 327675 e 65537 para obter 21474836475.

$$21474836475+1$$

Some 21474836475 e 1 para obter 21474836476.

$$21474836476$$

Fatorizar

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