Solve 3left(4+1right)left(4^2+1right)left(4^4+1right)left(4^8+1right)+1=4^16

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

Verify

Solution Steps

Add 4 and 1 to get 5.

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

Multiply 3 and 5 to get 15.

$$15\left(4^{2}+1\right)\left(4^{4}+1\right)\left(4^{8}+1\right)+1=4^{16}$$

Calculate 4 to the power of 2 and get 16.

$$15\left(16+1\right)\left(4^{4}+1\right)\left(4^{8}+1\right)+1=4^{16}$$

Add 16 and 1 to get 17.

$$15\times 17\left(4^{4}+1\right)\left(4^{8}+1\right)+1=4^{16}$$

Multiply 15 and 17 to get 255.

$$255\left(4^{4}+1\right)\left(4^{8}+1\right)+1=4^{16}$$

Calculate 4 to the power of 4 and get 256.

$$255\left(256+1\right)\left(4^{8}+1\right)+1=4^{16}$$

Add 256 and 1 to get 257.

$$255\times 257\left(4^{8}+1\right)+1=4^{16}$$

Multiply 255 and 257 to get 65535.

$$65535\left(4^{8}+1\right)+1=4^{16}$$

Calculate 4 to the power of 8 and get 65536.

$$65535\left(65536+1\right)+1=4^{16}$$

Add 65536 and 1 to get 65537.

$$65535\times 65537+1=4^{16}$$

Multiply 65535 and 65537 to get 4294967295.

$$4294967295+1=4^{16}$$

Add 4294967295 and 1 to get 4294967296.

$$4294967296=4^{16}$$

Calculate 4 to the power of 16 and get 4294967296.

$$4294967296=4294967296$$

Compare 4294967296 and 4294967296.

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