已知2ˆ96 -1可以被在60至70之间的两个整数整除,则这两个整数是多少?

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)=(2^48+1)(2^24+1)(2^12+1)×65×63所以这两个数是65和63