求证:2^48-1能被60—70之间的两个整数整除

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求证:2^48-1能被60—70之间的两个整数整除

求证:2^48-1能被60—70之间的两个整数整除
求证:2^48-1能被60—70之间的两个整数整除

求证:2^48-1能被60—70之间的两个整数整除
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)
=63*65*(2^12+1)(2^24+1)
所以2^48-1能被63和65整除.

2^48-1
=(2^24+1)(2^24-1)
=(2^24+1)(2^12+1)(2^12-1)
=(2^24+1)(2^12+1)(2^6+1)(2^6-1)
=(2^24+1)(2^12+1)×65×63

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)
2^6-1 = 63
2^6 +1 = 65
2^48-1能被60—70之间的两个整数 63, 65 整除