1 . 有__________ 个不超过2020的正整数k,满足对任意的正整数n,均有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9c9ff61597941cfa81be2ac40265667.png)
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2 . 对实数
,不超过
的最小值的最大整数为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14db6b568531ef989bb26227d54d3055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b02667b48e703f5a4cdae6201ee3458.png)
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3 . 设递推数列
满足:
,如果对任意的首项
且
,数列中一定存在某项
,则不超过
的最大整数是____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a50836192856e048e1fe207d0b61bc1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5224c5faa2f07d81db12c937e3a38d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4be043e433182a1255ef5bf2ff2c96fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe1593b8834ccf3f3ddd52a8deec97db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04a38189db22659e85d0baf16dbf5444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/085d58fb6a91ae4e7712dfa55baff725.png)
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4 . 方程
有___________ 组整数解.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2575e91a4d256f5413831810f99f332f.png)
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5 . 满足
的所有正实数x的整数部分之和是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3ced6125ae41187142764cb050df1cf.png)
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6 .
中,
,
,作
交
于D.已知
,
,设S为
的面积,则
写成最简分数之后,分子分母之和为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ff214d99784c6b23b7784bdaf3ed37a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58557422677059ad3eebf806022b203c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79e567a94f1d28a9c6693ba1ab89c8a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/909f43d5e0c217a24d0e71b91e6b9855.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c42f33bcd36071743aab327dda456f91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29315b499c8a01b20e1637b2add1dcbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ff214d99784c6b23b7784bdaf3ed37a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be8023be0e5d4851396c3fb663811beb.png)
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7 . 已知x,y,z是3个大于等于1的实数,那么
最小值写成最简分数后分子分母之和是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58fcd69b1c9e63b91b0274cc02b80c91.png)
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8 . 有_______ 组整数
满足
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de7deb1b206b4312834b68c937f652df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4daf262375a632f281952f4551ec4c63.png)
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9 . 已知函数
,使得任取实数x,y,z都有
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/445ca04eff5078b77fcb78234faf9207.png)
__________ .(其中
表示不大于x的最大整数).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a17e36b57a381a274173902e8a020d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5673732a290720249ab8011de7ca1c56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/445ca04eff5078b77fcb78234faf9207.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72e90b41a295a4b424cf37f5640430dc.png)
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10 . 设
的三个内角分别为A,B,C,假设
的最大值为
,将
写成最简分数后分子分母之和为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ff214d99784c6b23b7784bdaf3ed37a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd9abd7168399e6881800577a90c3b5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07c9121cede0ee0562e23b8a26b34616.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07c9121cede0ee0562e23b8a26b34616.png)
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