Вычислите
(2-1)(2+1)(2^²+1)(2^⁴+1)(2^8+1)-2^16

18_03_09_Задание № 1:

Вычислите (2−1)(2+1)(2^2+1)(2^4+1)(2^8+1)−2^16

РЕШЕНИЕ: (2−1)(2+1)(2^2+1)(2^4+1)(2^8+1)−2^16=(2^2−1^2)(2^2+1)(2^4+1)(2^8+1)−2^16=(2^2−1)(2^2+1)(2^4+1)(2^8+1)−2^16=(2^4−1^2)(2^4+1)(2^8+1)−2^16=(2^4−1)(2^4+1)(2^8+1)−2^16=(2^8−1^2)(2^8+1)−2^16=(2^8−1)(2^8+1)−2^16=2^16−1^2−2^16=-1

ОТВЕТ: -1