已知数列
满足
,
.给定奇质数
和正整数
满足
,证明:
的充分必要条件为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/909736dad505d81be43aef91e6309bf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5108053cdc0b7d5d1813bbf96689ae5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c226ece1d984f7733996dbe669b6875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6f95f1bdd88065ccc93d4f6410b9f3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/580fd18d9d137cf66ed9c24b91f6463c.png)
2019高三·全国·竞赛 查看更多[1]
更新时间:2018-12-28 20:45:22
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解答题-问答题
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较难
(0.4)
【推荐1】给定
个(
)互不相等的实数
,所有的
个和
(
,
,
)中互不相同的数恰好有
个的充分必要条件是
,
,…,
成等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5d0a73f50b3e4583f1c1b6d6bf0d18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f846d93390223b563770b676ee30b06c.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/059a6c5a965c335b8da05e697da2c7c2.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f97d4ad3c68d0a1b7ddad9b0a99ba48e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b71af6590f0f369c164a054a8b63bf6.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
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较难
(0.4)
【推荐1】设
是整数1,2,…,
的一个排列,且满足
(1)
;
(2)
.
记上述排列的个数为
. 试求
被3除的余数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f2b043b989216035c6fd985f1dd6a3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6685c96436af1055b0b60022b6ac26fe.png)
记上述排列的个数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38fcec7af3520884b173b29bda6c657a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0928fdf08b36d3867d60c4a769163110.png)
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【推荐2】已知函数
满足①
均大于0;②对于任意的
,
均为整数;③
.试判断,对于每个整数
是否为整数,并对你的结论给出论证.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/363b32cd053fc0d99c6054316c788fdf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d10449bc77d692a7270e0f20a68cdf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b2a9a675d8aaca772c6c17b4ef3de66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62b0674f15d84e56ddd6a9b300d81910.png)
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【推荐1】数列
的通项为
,
是
除以10以后的余数.试问
是否为周期数列?如果是,请求出
的最小正周期;如果不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85b0224059591a7789608f59cddf5ce1.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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【推荐2】试证明:集合
满足
(1)对每个
及
,若
,则
一定不是
的倍数;
(2)对每个
(
表示
在
中的补集),且
,必存在
,
,使
是
的倍数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f759b35c3da8ef009e6a023d287dadb1.png)
(1)对每个
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cc020b0997a2f37b214718112b79d8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93854be5bbd952dc21b0ffdbe03e7491.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edf2163f4f7a83bc64c60ed07785d3eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e61509eb1c1c505717119a70c1dd4d59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/878e89b6eca35e34c863e832a2c661db.png)
(2)对每个
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eba35506dbb943d8b92cb7100c48bc8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21778974e8491fe2a158e70b459217be.png)
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