1 . 使得
,且
的正整数对
的个数是.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faa8b2348e13736cdebebdf5b81f214e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f29374b547d4d6296ec9e9664212f73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
A.225 | B.228 |
C.231 | D.234 |
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2 . 若既约真分数
满足
,则称其为“理想分数”.那么,理想分数的个数为.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2122e3f1e76a635e58e4d54aa594c552.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5310a8fc5e462dd7b853307a67a8ad47.png)
A.337 | B.666 |
C.674 | D.1332 |
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3 . 已知正整数
、
满足等式
.则数
与
的情况是.
![](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/c5be519b8c14f4ae6f38dddd396ba026.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55405933a79b37b6498af53dd3570c36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dc4f882febb1325453fb50cc9806f9b.png)
A.都是有理数 | B.都是无理数 |
C.一个是有理数,一个是无理数 | D.以上三种情况都可能出现 |
您最近一年使用:0次
2006高三·浙江·竞赛
4 . 设 n(n < 150)是正整数 ,且 n3 + 23 能被 24 整除.这样的 n 有个.
A.6 | B.7 | C.11 | D.12 |
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2006高三·甘肃·竞赛
5 . 设
是互质的两个自然数.则
和
的最大公约数为.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/663a61ad241d5d874c9a9362f0ee917c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c925be255ca736a53b24d13ddede1a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe2b05214c8b22507f0c36b110593d0a.png)
A.1 | B.2 | C.1或2 | D.可能大于2 |
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2006高二·河南·竞赛
6 . 已知
、
、
都是质数,并且
有唯一的值和它对应,则
只能取.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17925653c433311ab7c4ccb5062bc36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaacfaef44a654c0a1c283ef03fc0550.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
A.40 | B.44 | C.74 | D.86 |
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7 . 已知a、b、c、d是偶数,且
,
,a、b、c成等差数列,b、c、d成等比数列,则a+b+c+d=.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16b98288d2e9f0694142bea687e1c740.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ed92e74c39845c4542ba6721dcc7575.png)
A.384 | B.324 | C.284 | D.194 |
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8 . 若两个整数
、
满足方程
,①就称数组
为方程①的一组整数解.则方程①的整数解的组数为.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/456a479ea600e938778f38f8796ee014.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82a79a33a83a7ba57a34b5093d1d1d02.png)
A.0 | B.1 | C.2 | D.2006 |
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9 . 已知自然数
不是5的倍数.则5除
,
时,有.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfab9d144cdaf7dcf5dd7e445fdeca45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fd8ba6639589dacee1706f71d3c296d.png)
A.![]() ![]() |
B.![]() ![]() |
C.![]() ![]() |
D.不能确定,都有可能发生 |
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10 . 使
和
都是整数的正数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c58c11fe9b7eb5712c343860f63a5e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6158fbaa75c814ff16998ffa8b04ead4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
A.不存在 | B.只有一个 | C.只有两个 | D.有无穷多个 |
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