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Re:怎样证明是2^k 呢?

Posted by gsyagsy at 2007-09-09 19:53:25 on Problem 3372 and last updated at 2008-09-04 19:23:08
In Reply To:怎样证明是2^k 呢? Posted by:enter2004 at 2007-09-09 19:12:15
> 怎样证明是2^k 呢?
ak=1+(k-1)*k/2
ai如果和aj同余于n
则ai-aj=(i-j)(i+j-1)/2为n的倍数
然后可以
1。分析n为奇数a1到an中有同余的,并且a(i+n)=ai(mod n)
显然遍历不了0至n-1
2。然后n为偶数时,i-j和i+j-1奇偶不同
   n=t*2^s
   t!=1 总能找到i>j,i,j在0到n之间使ai=aj(mod n)
   而a(i+n)=ai+n/2(mod n) a(i+2*n)=ai(mod n)
   知道遍历不了……
再往下分析就是……这只是个大概
  

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