1 . 设数列
满足
,且对任意整数
是最小的不同于
的正整数,使得
与
互质,但不与
互质.证明:每个正整数都在
中出现.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f79ae17a7a504d6b0998364c13a9e0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27cab8c94c52ac4170c6617790361246.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a7170836b85b2aad29b01f1af0e86d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7230de53663c75658c58bbf206a0085.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bed25da42194b5a81d123933d5704f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
名校
解题方法
2 . 设函数
.
(1)证明:存在唯一的函数
,使得
;
(2)求所有的非负实数
使得
;
(3)
,
(i)证明:关于
的方程
与
都有唯一实根;
(ii)记
分别为方程
,
的实根,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041fc0e0ff542027634491e686a510b6.png)
(1)证明:存在唯一的函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2ee09653f053eccbba4b85fbf97c3e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aca8208f53be6a7033b4fd2a11c7964.png)
(2)求所有的非负实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f8bfb563f79688d136e0cb958b5153c.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb1523685c2d0a9ef21660908378ac90.png)
(i)证明:关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/713c59f274e9146b6d85375435315521.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3a4cb45ca6e42ced4a5c4026e2290f8.png)
(ii)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd8ca3aa2d1ba52e82613d0d65d800e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/713c59f274e9146b6d85375435315521.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3a4cb45ca6e42ced4a5c4026e2290f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3c414bc882fb3c5e364582886c3325c.png)
您最近一年使用:0次