2023高三·全国·专题练习
1 . 已知素数
证明:
为整数,其中
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78ede915be033958bbbc49cad146be35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4af8969d81e3649f3c453758ff275340.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e396e106da8f2ec43475cd0aa7257da.png)
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2023高三·全国·专题练习
2 . 求证:
为任意整数
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de16fdd14f9f111f1ec41514d234fa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
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2023高三·全国·专题练习
3 . 设
是正整数,
(1)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/182c38174d9345986d8cb38cdf8217a4.png)
(2)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f14e67260b7ce9fb9a1fba4d23e7b3.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/182c38174d9345986d8cb38cdf8217a4.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f14e67260b7ce9fb9a1fba4d23e7b3.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/847e7fba99adadf43d8429c2598823be.png)
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2023高三·全国·专题练习
4 . 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
5 . 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
6 . 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)
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2023高三·全国·专题练习
7 . 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)
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2023高三·全国·专题练习
8 . 意大利数学家斐波那契的《算经》中记载了一个有趣的数列:
,
,
,
,
,
,
,
,
,
,
,
,
,这就是著名的斐波那契数列,该数列的前
项中奇数的个数为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3304e23f3b0f9569c4140ca89b6498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5453184e251cfe787b5965cd38426962.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1834490aacbee800ed5721312f4be1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fd1a0475c383701348a36c35aea32f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92128c6c226ce688bc160fb86854f2fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/796e3e32d29652fb3ed9984c414aec35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/459cc36d02d31815ba9f2d05e130e0cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07096af3b99fd1cb11c31f19a2c6408e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d01dd350dc95f42f1883e0cc7aae084.png)
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2023高三·全国·专题练习
9 . 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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