因數分解 指數相關的問題 - 拼圖
By Candice
at 2004-11-09T23:34
at 2004-11-09T23:34
Table of Contents
※ 引述《purplesand (purplesand)》之銘言：
: 兩題
: 1. A=8765 B=76543 A*B=?
直接乘最快 ^^;
: 2. 介於50到75之間且是2的48次方-1的因數是?
: 請問有什麼好的解法嗎???
2^48-1 = (2^24-1) * (2^24+1)
= (2^12-1) * (2^12+1) * (2^24+1)
= (2^ 6-1) * (2^ 6+1) * (2^12+1) * (2^24+1)
= (2^ 3-1) * (2^ 3+1) * (2^ 6+1) * (2^12+1) * (2^24+1)
= 7 * 9 * (2^ 6+1) * (2^12+1) * (2^24+1)
所以至少7*9=63一定是2^48-1的因數
--
: 兩題
: 1. A=8765 B=76543 A*B=?
直接乘最快 ^^;
: 2. 介於50到75之間且是2的48次方-1的因數是?
: 請問有什麼好的解法嗎???
2^48-1 = (2^24-1) * (2^24+1)
= (2^12-1) * (2^12+1) * (2^24+1)
= (2^ 6-1) * (2^ 6+1) * (2^12+1) * (2^24+1)
= (2^ 3-1) * (2^ 3+1) * (2^ 6+1) * (2^12+1) * (2^24+1)
= 7 * 9 * (2^ 6+1) * (2^12+1) * (2^24+1)
所以至少7*9=63一定是2^48-1的因數
--
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