2023高三·全国·专题练习
1 . 若
证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea722d76386a47ab303d830d890ae6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f1cecadde7302929cb3e1117f0625de.png)
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2023高三·全国·专题练习
2 . 若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea722d76386a47ab303d830d890ae6aa.png)
跑遍模
的简系,
跑遍模
的简系.证明:
跑遍模
的简系.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea722d76386a47ab303d830d890ae6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77ab1256702aef4e9f1a5eb6c12ecc96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fbd67f60f04c278bdd867fdb3979dfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5000a896e35177ba104a90a428061722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99e0a6a2bd38c553771889d0821fb868.png)
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2023高三·全国·专题练习
解题方法
3 . 已知数列
满足
.
(1)证明:
是正整数数列;
(2)是否存在
,使得
?并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaa39c95c48104697357b8f0e98c9840.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)是否存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24f8494594299d0ecce6e1e52151f402.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d3ca83b04f476083c4044c33347a038.png)
您最近一年使用:0次
2023高三·全国·专题练习
4 . 已知数列
满足
.
(1)证明:
是正整数数列;
(2)是否存在
,使得
?并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df3f0a8c6cf53d0b0b71ccf8e6f5226a.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)是否存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc466f4022d38bf434544641fae2b51c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c4122bdc1b2a61097735c85b2dd655c.png)
您最近一年使用:0次
2023高三·全国·专题练习
5 . 已知数列
满足
.
(1)证明:
是正整数数列;
(2)是否存在
,使得
?并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df3f0a8c6cf53d0b0b71ccf8e6f5226a.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)是否存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39891fee58e55b44b4103f46c3608891.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c4122bdc1b2a61097735c85b2dd655c.png)
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2022高三·全国·专题练习
6 . 已知0≤n≤18,19m+n=20212022,则n=__ .
您最近一年使用:0次
7 . 已知正整数
不超过2022且满足100整除
,则这样的
的个数为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c00a9c44e9667fac20df7b172b10626f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
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8 . 求所有素数p,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63de2bc403dd111b66c524ae1843d1b1.png)
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9 . 存在正整数数对(a,b)满足
的正整数k的个数为_______ .([a,b]表示正整数a与b的最小公倍数)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c887a7a8993e5e0b99639af7f3fa7d9c.png)
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10 . 求满足
的所有正整数对
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7472fd6abdb28f2c670628e4ed9db5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ceb955cff0a243b938fe2d2d1e8a5dc.png)
您最近一年使用:0次