Question

已知2的96次方-1可以被60至70之间的的两个整数整除,则这两个整数是多少?

Answer 1

2^96-1

=(2^48+1)(2^48-1)

=(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

所以两个数是65和63