1 . 有两个正整数x,
,其最大公约数与最小公倍数之和等于这两个数的积与和的差,则:
(1)满足条件的数组
共有______ 个;
(2)在所有满足条件的数组
中,
的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec5464d439362506b5a7fd9b0db67c06.png)
(1)满足条件的数组
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82a79a33a83a7ba57a34b5093d1d1d02.png)
(2)在所有满足条件的数组
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82a79a33a83a7ba57a34b5093d1d1d02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88584cf1df43e28d03592c7998b1653.png)
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2 . 设
是正整数,
是素数,
且
整除
,证明:
整除
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20dd7cdef44777d41d74d699ffdd746d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ff4dd0a72bbcaec33d151ac1365d663.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d2d7ddd7ef3b6cde30018bc6a84b9e0.png)
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3 . 设正整数
,且
是完全平方数,则可能的n的个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d93a22c60e7efecc16849f7769563ef4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a7ca0f71fcb392a96c8d8c8d2f83811.png)
A.1 | B.2 | C.3 | D.以上答案都不对 |
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4 . 已知
,则S的个位数字是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e599e7dcc246a1b1c418e1dec13a256b.png)
A.4 | B.5 | C.7 | D.以上答案都不对 |
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5 . 设
,若
,则n的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75ede22f9a56e516144c5855a0f1ad55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891697449991fae3c1881de86e4a6714.png)
A.71 | B.72 | C.80 | D.81 |
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6 . 方程
的正整数解
的组数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef047f21cf0672fe9dfe94c5b9cc3296.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d685c54089867c395a4c49ba01b1237.png)
A.0 | B.2 | C.无穷多 | D.以上答案都不对 |
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7 . 已知
为正整数.
(1)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e881a784e2b5216ba5562e07c4553a4e.png)
不能 表示为两个以上连续整数的乘积;
(2)若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e881a784e2b5216ba5562e07c4553a4e.png)
能 表示为两个连续整数的乘积,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e881a784e2b5216ba5562e07c4553a4e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e881a784e2b5216ba5562e07c4553a4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2023-02-15更新
|
162次组卷
|
2卷引用:安徽省宣城市泾县中学2021年强基夏令营选拔测试数学试题
8 . 已知
表示不超过x的最大整数,则
的值域为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38578960d77ac60f61f703e209437e1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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9 . 已知
是常数项不为0的整系数多项式,
,则
中有_________ 项为0.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bab05f010cb02bcb2ccd0e0297d7988.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/877e80920e2a85c8bd3f7d53bd5187ec.png)
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10 . 若正整数m,n满足
,则
有_________ 组.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01f9269609deac0f03b2d6ed9ef614cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a64d924836b4292239d9726c6473d7f5.png)
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