Question

Hu

求解

試計算下列各式:
(1) (5−1 ) ( 5+1) (5²+1 ) ( 5¹+1 ) +1 = ?
(以指數表示)
(2) 若1×3×(2+1)(2+1)(2+1)= 2'-1,
求n=?
fie

Answer 1

Mer

(5^2 - 1)(5^2 + 1)(5^4 + 1) + 1
= (5^4 - 1)(5^4 + 1) + 1
= (5^8 - 1) + 1 = 5^8

Mer

將 1 * 3 改成 4 - 1 = 2^2 - 1
(2^2 - 1)(2^2 + 1)(2^4 + 1)(2^8 + 1)
= (2^4 - 1)(2^4 + 1)(2^8 + 1)
= (2^8 - 1)(2^8 + 1)
= 2^16 - 1
所以 n = 16