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

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

Baholash

$$21474836476$$

Yechim qadamlari

\left(2^{2}+1\right)^{2} hosil qilish uchun 2^{2}+1 va 2^{2}+1 ni ko'paytirish.

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

3 olish uchun 2 va 1'ni qo'shing.

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

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

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

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

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

2 daraja ko‘rsatkichini 5 ga hisoblang va 25 ni qiymatni oling.

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

75 hosil qilish uchun 3 va 25 ni ko'paytirish.

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

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

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

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

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

1275 hosil qilish uchun 75 va 17 ni ko'paytirish.

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

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

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

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

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

327675 hosil qilish uchun 1275 va 257 ni ko'paytirish.

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

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

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

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

$$327675\times 65537+1$$

21474836475 hosil qilish uchun 327675 va 65537 ni ko'paytirish.

$$21474836475+1$$

21474836476 olish uchun 21474836475 va 1'ni qo'shing.

$$21474836476$$

Omil

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