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

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

Baholash

$$6004800933418326$$

Yechim qadamlari

2 daraja ko‘rsatkichini 2 ga hisoblang va 4 ni qiymatni oling.

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

5 olish uchun 4 va 1'ni qo'shing.

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

4 daraja ko‘rsatkichini 2 ga hisoblang va 16 ni qiymatni oling.

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

17 olish uchun 16 va 1'ni qo'shing.

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

85 hosil qilish uchun 5 va 17 ni ko'paytirish.

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

8 daraja ko‘rsatkichini 2 ga hisoblang va 256 ni qiymatni oling.

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

257 olish uchun 256 va 1'ni qo'shing.

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

21845 hosil qilish uchun 85 va 257 ni ko'paytirish.

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

16 daraja ko‘rsatkichini 2 ga hisoblang va 65536 ni qiymatni oling.

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

65537 olish uchun 65536 va 1'ni qo'shing.

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

1431655765 hosil qilish uchun 21845 va 65537 ni ko'paytirish.

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

22 daraja ko‘rsatkichini 2 ga hisoblang va 4194304 ni qiymatni oling.

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

4194305 olish uchun 4194304 va 1'ni qo'shing.

$$1431655765\times 4194305+1$$

6004800933418325 hosil qilish uchun 1431655765 va 4194305 ni ko'paytirish.

$$6004800933418325+1$$

6004800933418326 olish uchun 6004800933418325 va 1'ni qo'shing.

$$6004800933418326$$

Omil

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