智力题以及概率题 - Backyard of LixinZhang


智力题以及概率题 - Backyard of LixinZhang

一个是如果两个质数中间只有一个数，那么证明他能被6整除？

分析

G,E,A,B,C,D,F

  • 设三个数为A,B,C。因为A,C为质数，一定不是偶数，则B一定为偶数。
  • 因为不长为三的一定会出现被3整除的数字，由于A,C为质数不能被三整除，因此A的左边E和C的右边D一定不能被三整除。
  • 那么E的左边G必须能被3整除，因为不能可能连续的3个数都不能被三整除，因此B=G+3，能被3整除，其又能被二整除，因此必须能被6整除，证毕。

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