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)

 

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