1 . 集合
、
为
的一个等浓二分划(即
,
,且
.记集合
中所有数的积为
,集合
中所有数的积为
,称
为
的等浓二分划的特征数.证明:
(1)集合
的等浓二分划的特征数一定为合数;
(2)若等浓二分划的特征数不为2的倍数,则该特征数为
的倍数.
注:有限集合
的元素个数简记为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e375894300650a0aabf113ee94ad048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07d037e9d6288bf61a1fceed25a419df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71e896f2fa4f85dc29f7e71d7e0f6d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/952a56c457caee8c2a1c7fec94641eca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/316d25dfa1b73fc02e1b8cfaf3adfcb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
(1)集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
(2)若等浓二分划的特征数不为2的倍数,则该特征数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f8fde3a2003ef44fdc891265c68cea.png)
注:有限集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e565dc1dd0d9cc3e4186cd614814b7f6.png)
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2 . 记自然数
的数字和为
.则方程
的解集为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3888740fa8b552b55b4a0c8ae4166007.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b30756ef357d19802348374b4a13bbb8.png)
您最近一年使用:0次