1 . 设整数
满足
,且对任意整数
是24的倍数,则满足条件的有序数组
的个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c14d9ae06f864498048d55088ff4e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8f47a822f34e848ebedd6c82ff2c0cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b02438649ad14b8de1e9ef5b5dda340.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c2a29087dbd2e7635da13f7d288c1c.png)
A.12个 | B.24个 | C.36个 | D.48个 |
您最近一年使用:0次
2 . 一个正整数n称为具有“
因数积性质”:若n的所有正因数的乘积等于
,则不超过400的正整数中具有“
因数积性质”的数的个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4815b8b7203fb465809b395153ea3340.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411a315870ed3e6d0e8ea885f1a04bcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4815b8b7203fb465809b395153ea3340.png)
A.55 | B.50 | C.51 | D.前三个答案都不对 |
您最近一年使用:0次
3 . 已知集合
,记
,满足
的数对
的个数记为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/007767c18d872cb34b490c8b0b3151dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8865f23cb7e7665c6c728a798268b111.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5037ef598cf26b9f7e2c6e08906f3e92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4b3392579424244c50ddf416ee3434d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1b1db69a2028e7dccc1e4e3b7291b5.png)
A.![]() |
B.![]() |
C.![]() |
D.![]() |
您最近一年使用:0次
4 . 设
,集合T是S的n元子集,且其中任意两个元素互质,对任意符合要求的集合T,均至少包含一个质数,则n的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ad00448af8ca9fd26e0f3484f4876da.png)
A.15 | B.16 | C.17 | D.18 |
您最近一年使用:0次
5 . 已知不定方程
有正整数解,则正整数n的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d073ff0af0166c338f9b66d59d4adb.png)
A.11 | B.13 | C.15 | D.17 |
您最近一年使用:0次
6 . 满足方程
的有序正整数组
的个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/094b091f73308f4ea1b0b85d33ffe1fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0203b006524305c3d8ee0b6c34cd872b.png)
A.12 | B.13 | C.24 | D.25 |
您最近一年使用:0次
7 . 在
的全体正因数中选出若干个,使得其中任意两个的乘积都不是平方数则最多可选因数个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb1d161869928ced3f945a6380029ad6.png)
A.16 | B.31 | C.32 | D.前三个答案都不对 |
您最近一年使用:0次
8 . 已知正整数
,
,
,
满足
,则
的值有可能等于( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62948164bee4ec540287564f801269a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6bb99e2251df1777c5288d603170bd2.png)
A.101 | B.301 | C.401 | D.以上三个都不对 |
您最近一年使用:0次
9 . 对任意正整数
,定义
为使得
是
的倍数的最小正整数
.关于下列三个命题:
①若
为奇质数,则
;
②对任意正整数
,都有
;
③对任意正整数
,都有
.
其中所有真命题的序号为( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f378b8bfaacc38d98321122c1ed7c927.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f42753ada77daee9f575ad735e05462c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/626674c321964b32bb6d31f8d712a1d3.png)
②对任意正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fec80a250e8f692c8322aa4e2773235.png)
③对任意正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6a0cff970343dbc4fdf533643c42db6.png)
其中所有真命题的序号为( ).
A.①② | B.①③ | C.②③ | D.①②③ |
您最近一年使用:0次
10 . 满足对所有的
,1,…,
,都有
与2007互质的正整数
的数目有( )个.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1487f4b936e5f924fa6b1ea298e302f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42c8e77221e7bc2e2476c091c654d098.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
A.3 | B.5 | C.7 | D.9 |
您最近一年使用:0次