定义“二元函数”如下:
;例如:
,对于奇数m,若任意
,存在
为正整数,且
(
彼此不同),满足
,则最小的正整数m的值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3966fa557dd02ae0fa942956d4d3979.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/378403dc180c610910ec61e5faf9bb27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aa9489cb77fac183fb891b291d02009.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d59a31a27f71f3351780a75bb6fd224.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5a9d3dc3d131c7bdc168c2d6198d158.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/575f0017700c3081f3b0adfe313fdff9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc0106a86de4798c11ca5c7e672c9f6e.png)
更新时间:2022-06-28 12:13:44
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【推荐1】等比数列
的相邻两项
,
是方程
的两个实根,记
是数列
的前
项和,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7978d7bd6f6caf9ac9837ffce5f89654.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090426eb29836bc30c006b3739c08057.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7978d7bd6f6caf9ac9837ffce5f89654.png)
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【推荐2】已知三角形数表:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/9/41a681e0-33a8-45d3-a8d3-ec50a6044c5a.png?resizew=173)
现把数表按从上到下、从左到右的顺序展开为数列
,记此数列的前
项和为
.若
,则
的最小值是_____ .
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/9/41a681e0-33a8-45d3-a8d3-ec50a6044c5a.png?resizew=173)
现把数表按从上到下、从左到右的顺序展开为数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/287b755d2ab06e7a01a9cb3fbcd41d88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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【推荐1】德国著名数学家狄利克雷在数学领域成就显著,他是数学史上第一位重视概念的人,并且有意识地“以概念代替直觉”,以其名命名的函数
称为狄利克雷函数,现定义一个与狄利克雷函数类似的函数
为“L函数”,则关于狄利克雷函数和L函数有以下四个结论:
①
;
② 函数
既是偶函数又是周期函数;
③ L函数图象上存在四个点A、B、C、D,使得四边形ABCD为矩形;
④ L函数图象上存在三个点A、B、C,使得△ABC为等边三角形.
其中所有正确结论的序号是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21217544248fd97e0cb121b2fc03ba01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1df3facdc8320278f593bbe469f84f2b.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cf0f509ce7d3bd9f929954e8aa6f51b.png)
② 函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2f5a719332bc8af83fbe70fa6cf632d.png)
③ L函数图象上存在四个点A、B、C、D,使得四边形ABCD为矩形;
④ L函数图象上存在三个点A、B、C,使得△ABC为等边三角形.
其中所有正确结论的序号是
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【推荐2】给出下列四个命题:①命题“
”为真,则实数
的范围是
;②设
,则“
”是“
”的充要条件;③关于
的方程
,存在实数
,使得方程恰有5个不同的实根;④函数
的定义域为D,若满足:(1)
在D内是单调函数;(2)存在
,使得
在
上的值域为
,那么就称函数
为“梦想函数”.若函数
是“梦想函数”,则t的取值范围是
;其中真命题有_________ (填序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8983faa5adf0008b8d69c64cf3518f44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73254f32b6da29ecc32df2e9f87a4c97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a46e678bf9d2df5ad4c782b3dc22f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc548fd3964424e7745160d89488326.png)
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