解题方法
1 . 已知:正整数列
各项均不相同,
,数列
的通项公式![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f44d3c3cbd26b797a70e5fd060f3106.png)
(1)若
,写出一个满足题意的正整数列
的前5项:
(2)若
,求数列
的通项公式;
(3)证明若
,都有
,是否存在不同的正整数
,j,使得
,
为大于1的整数,其中
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de777c4e44546bcfe26ad5b6bb418052.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f44d3c3cbd26b797a70e5fd060f3106.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9a7269903c6005c0645a6033c8c1dd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d11adcab5f73046ada2b4dd21ba74614.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)证明若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21d2e7f3d5771184a5a93749368dc2a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f33e3c5a9ab39e55e78d6aef60e5e3d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b97c28585cf80e2b403c8e23ac391573.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2690c409f513b571c3c2548228536d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b204cd055cc01b4fc9dd888b8348d12.png)
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