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公式的推导

Posted by Ly86 at 2010-04-25 19:03:36 on Problem 2140
假设a,a+1,a+2...a+k ,为一组符合的答案
有
(k+1)a+0.5*k*(k+1)=n成立
划成
(a + 0.5*k)(k+1)=n
观察等式发现必须满足
1. 0.5*k为整数. 所以k是偶数
2. (k+1) 为n的因数,并且 (k+1) 为奇数
所以综上
n有多少个奇因数,就是本题的答案

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