2023高三·全国·专题练习
1 . 已知两个自然数b和c及素数a满足方程a2+b2=c2.证明:这时有a<b及b+1=c.
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2 . 求所有正整数
,使得给定序列
,
,中的每一项都是平方数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/550904843e7d2f286f7a72997cd21393.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f14192117991bd1440464548d6e689ee.png)
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3 . 试问:能否把
表示成
的形式?其中
、
均为大于
且小于
的正整数,
均为两两不相等的小于
的正有理数,
均为大于
且小于
的正整数,同时,
两两不相等.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1d31920144a0ab05e051c302319bf27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74245d94fe81c3fd8156cbd5746782be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0efba7147f5b9ced8bc4a72f0a9fb8af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e9e34683ae906ff0b4644539b2d313b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c70a11ffd6ff9186f80b057efcccb4d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dba98b6472af674e68d6293a0baaf926.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da67a7d660a6740a39e19d0b462ac047.png)
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