1 . 设数列
满足
,且对任意正整数
均有
.求
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13a6e1d671215fc96e4bee3541d1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6324f5c2c73bdcac4e9154429ac79baa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
您最近一年使用:0次
2 . 某个会议有若干人(至少3人)参加,现要将这些人分组.分组前,每个人都选择两个人.若被选择的两个人同组.则选择他们的人不能在这组中.求最小的正整数
,使无论有多少人参加,且无论每人如何选择,都可以将他们按要求分成
组.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
3 . 给定正整数
.求最大的实数
.使得
对任意正实数
恒成立,其中
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/526e037512bd10e65ebd99b73aa26341.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9304e71a623c4412188a800046a970d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/897b606fdc64a88a0938d3d60c3ea3e9.png)
您最近一年使用:0次
4 . 设
是整数.对每个正整数
,令
为
在
进制表示下的非零数字的个数.证明:对于任意给定的正整数
和
,存在正整数
使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/731bdc8d2686a05f12a2ba8a7e3b01be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d1748a0e5fba63eac995e4388bb537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5809edaae5fd443ff3126d8ad0eaa1b5.png)
您最近一年使用:0次
5 . 给定整数
.求具有下列性质的最大常数
,若实数列
满足:
,则
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af0dc284b8b34f03783c2207e35cf626.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c67135f5e426945425bcfc0d0e167a72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b0700b44523ab8cc957bdcb1721367d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bcebc0ae9b76e0ef2ee54385dc9c83a.png)
您最近一年使用:0次
6 . 设n为不小于3的正整数,在正n边形中,选取一些对角线,满足其中的任两条对角线若在多边形内部相交则一定垂直.问:最多可选取多少条对角线?
您最近一年使用:0次
7 . 求最小的正整数
,使得当正整数点
时,在前
个正整数构成的集合
中,对任意
总存在另一个数
且
,满足
为平方数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d2ba3c51d2726df8cee0918b8af2d32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcc6a0568db5a3fc7aca3366e608cf69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acfc595518cf752e1c7903dfff93dbda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7580ce638933a1c81da5e2e1b656c77a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7741c8d8f0486556a102d904fb26a7be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88584cf1df43e28d03592c7998b1653.png)
您最近一年使用:0次
8 . 求正整数n的最大值,使得对任意一个以
为顶点的n阶简单图,总能找到集合
的n个子集
,满足:
当且仅当
与
相邻.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07bcd047595eb49ca5978ee91b3c33aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e8c80883caf31045f1aa796c679a0c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/252bab154aa5bdc9b4bce4c0d43aaf73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5da8bec0aeeab406ccb815a85cce9d81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0539fe8b83a5427649b7a52216112cb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f323258ad650bbd6228f50643c8457cd.png)
您最近一年使用:0次
9 . 求最小的正整数
,使得存在一个
的数阵满足如下条件: (1)每一个数均属于集合
; (2)记
为数阵中第
行中的数组成的集合,
为第
列中的数组成的集合
,则
,
是4026个不同的集合.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5311a22867a26d56314456b295cc0d9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d878c148fbe54dd59228fbf86eeb80ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f95e54a9b7c66c97dc6ee6161a25c0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/407f2faadb10cd787d49783b06a32462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7600d2cfbdc6146db96cc545706004f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9238f5a421fdf8ba4c8a1a6642d50c93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81c273738a6cf6d268972acf713ca617.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9446a03ba0ba93f26ed79ab43cf3dbd8.png)
您最近一年使用:0次
10 . 已知
,令
求
能取到的不同的整数值的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d4e786a33522b7aefe882287b08e3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0de0e2b8d9624c41f309cc348d932498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
您最近一年使用:0次