1道数学题目在线========

来源：百度知道 编辑：UC知道 时间：2024/05/28 00:15:19
已知2^96-1可以被60~70之间的2个整数整除,这两个数是多少?
请详细解答

平方差公式
2^96-1
=(2^48-1)(2^48+1)
=(2^24-1)(2^24+1)(2^48+1)
=(2^12-1)(2^12+1)(2^24+1)(2^48+1)
=(2^6-1)(2^6+1)(2^12+1)(2^24+1)(2^48+1)
=(2^3-1)(2^3+1)(2^6+1)(2^12+1)(2^24+1)(2^48+1)
=7*9*65*....
=63*65*...

显然2^48+1>2^24+1>2^12+1>70
所以这两个数是63和65

2^96-1
=(2^48+1)(2^48-1)
=(2^48+1)(2^24+1)(2^24-1)
=(2^48+1)(2^24+1)(2^12+1)(2^12-1)
=(2^48+1)(2^24+1)(2^12+1)(2^6+1)(2^6-1)

其中(2^6+1)(2^6-1) 是63和65