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

Question

упростите:

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

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