упростите:

1 * (2+1) (2^2+1) (2^4+1) (2^8+1) (2^16+1) (2^32+1) (2^64+1)

Question

Алгебра

Иля

2 мая, 14:05

упростите:

1 * (2+1) (2^2+1) (2^4+1) (2^8+1) (2^16+1) (2^32+1) (2^64+1)

+1

Ответы (1)

Знаете ответ?

Данило · Answer 1

A = 1 * (2+1) (2^2+1) (2^4+1) (2^8+1) (2^16+1) (2^32+1) (2^64+1)

надо упростить

1

(2+1) = 3 = (4-1) = (2^2 - 1)

(2^2 - 1) (2^2+1) = (2^4-1)

(2^4-1) (2^4+1) = (2^8-1)

(2^8-1) (2^8+1) = (2^16-1)

(2^16-1) (2^16+1) = (2^32-1)

(2^32-1) (2^32+1) = (2^64-1)

(2^64-1) (2^64+1) = (2^128-1)

1 * (2^128-1)

B = (2^128-1) - окончательный вид

проверка

A = 340 282 366 920 938 463 463 374 607 431 768 211 455

B = 340 282 366 920 938 463 463 374 607 431 768 211 455

упростите:1 * (2+1) (2^2+1) (2^4+1) (2^8+1) (2^16+1) (2^32+1) (2^64+1)

упростите:

1 * (2+1) (2^2+1) (2^4+1) (2^8+1) (2^16+1) (2^32+1) (2^64+1)