已知2的96次方-1可以被在60至70之间的两个数整除,则这2个数是多少?

Question

已知2的96次方-1可以被在60至70之间的两个数整除,则这2个数是多少?

Answer 1

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
所以这两个整数是65和63
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