1 . 设p为素数,对任意的非负整数n,记
,
,其中
,如果非负整数n满足
能被p整除,则称n对p“协调”.
(1)分别判断194,195,196这三个数是否对3“协调”,并说明理由;
(2)判断并证明在
,
,
,…,
这
个数中,有多少个数对p“协调”;
(3)计算前
个对p“协调”的非负整数之和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1538e59a0527883bb6ff5f5a5eb8e68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0dd417ec70cf425efddea5f4c7ba7b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ded2da98f74d955ff5dd8f9ac051968b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/208ffeb1f7342c141f490e3185d11930.png)
(1)分别判断194,195,196这三个数是否对3“协调”,并说明理由;
(2)判断并证明在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/366cfc0dec131eacf81cb194da71eb2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e60c0322d41827fa6dc18ee22de5e769.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03d950956eba112b45bb5b0a26393c07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fe9ad3cf2737677a9d3f1fb9fb2d2b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/223ec16c7b0b7d25431d352d89215462.png)
(3)计算前
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/223ec16c7b0b7d25431d352d89215462.png)
您最近一年使用:0次
2 . 莫比乌斯函数在数论中有着广泛的应用.所有大于1的正整数
都可以被唯一表示为有限个质数的乘积形式:
(
为
的质因数个数,
为质数,
),例如:
,对应
.现对任意
,定义莫比乌斯函数
(1)求
;
(2)若正整数
互质,证明:
;
(3)若
且
,记
的所有真因数(除了1和
以外的因数)依次为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e046acc0e785892df1ef03a440b0fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb5c607987b73502db63f77c9799f4bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08fe943e1acfb453f41bee79119cce60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38261aad19184a74c797b6b88ffd344d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86cb09df4dbbe40a2b7ed54da17346dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09881de0dc186bbcd1e60eb00159ee97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b5872b44498c348c023828ed66e86d1.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9b2c4263428e2ee419589171f27e23f.png)
(2)若正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/201e0fbcfb6833c4b1917cfed3096b6f.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10e468312d09c6563c9094b710a35a65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a4a887eaea7f0aac8505ed3b3c0c678.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4811e3603e8790c25aaf91c41d7c7f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/202a57af91d5be04e95fcbdb8f2b788f.png)
您最近一年使用:0次
2024-03-26更新
|
1289次组卷
|
5卷引用:河南省南阳市西峡县第一高级中学2023-2024学年高二下学期第一次月考数学试卷
河南省南阳市西峡县第一高级中学2023-2024学年高二下学期第一次月考数学试卷重庆市乌江新高考协作体2023-2024学年高二下学期第一阶段学业质量联合调研抽测(4月)数学试题湖南省衡阳市2024届高三第二次联考数学试题(已下线)压轴题08计数原理、二项式定理、概率统计压轴题6题型汇总(已下线)【人教A版(2019)】高二下学期期末模拟测试A卷
名校
3 . 定义:最高次项的系数为1的多项式P(x)=xn+an﹣1xn﹣1+…+a1x+a0(n∈N*)的其余系数ai(i=0,1,…,n﹣1)均是整数,则方程P(x)=0的根叫代数整数.下列各数不是代数整数的是( )
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
4 . 已知关于
的方程
有两个正整数根(
是整数).
的三边
满足
.求:
(1)
的值;
(2)
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47392055fa0c87222d942e60cb9e4c90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2750957c5331e1a55e6120a20bbe2a9.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
您最近一年使用:0次
2022-08-28更新
|
201次组卷
|
3卷引用:2023年新东方高一上数学05