Применяем несколько раз формулу разности квадратов:
(a-b)(a+b)=a²-b²
1)
(2-1)(2+1)(2²+1)(2⁴+1)(2⁸+1)-2¹⁶ =
= (2²-1)(2²+1)(2⁴+1)(2⁸+1)-2¹⁶ =
= (2⁴-1)(2⁴+1)(2⁸+1)-2¹⁶ =
= (2⁸-1)(2⁸+1)-2¹⁶ =
= (2¹⁶-1) - 2¹⁶ = 2¹⁶-1 - 2¹⁶ = - 1
ответ: -1.
2)
(2+1)(2²+1)(2⁴+1)(2⁸+1)(2¹⁶+1)-2³² =
= 1*(2+1)(2²+1)(2⁴+1)(2⁸+1)(2¹⁶+1)-2³² =
= (2-1)(2+1)(2²+1)(2⁴+1)(2⁸+1)(2¹⁶+1)-2³² =
= (2²-1)(2²+1)(2⁴+1)(2⁸+1)(2¹⁶+1)-2³² =
= (2⁴-1)(2⁴+1)(2⁸+1)(2¹⁶+1)-2³² =
= (2⁸-1)(2⁸+1)(2¹⁶+1)-2³² =
= (2¹⁶-1)(2¹⁶+1)-2³² =
= (2³²-1)-2³² =
= 2³²-1-2³² = -1
ответ: -1.
1)1*3*5*17*257-(2^8)²=65 535-65 536=-1
2)3*5*17*257*65 537-(2^8)^4=4.294.967.295-4 294 967 296=-1
