Question

Доведіть, що (2 + 1)(2^2 + 1)(2^4 + 1)(2^8 + 1)(2^16 + 1) = 2^32 – 1.

Answer 1

a² - b² = (a - b)(a + b)

домножаем на 1 левую часть

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