1 . 两个数互素是指两个正整数之间除了1之外没有其他公约数.欧拉函数
(
)的函数值等于所有不超过正整数n,且与n互素的正整数的个数,例如
,
.
关于欧拉函数给出下面四个结论:
①
;
②
,恒有
;
③若m,n(
)都是素数,则
;
④若
(
),其中
为素数,则
.
(注:素数是指除了1和它本身以外不再有其他因数,且大于1的正整数.)
则所有正确结论的序号为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbc89a53c03cb86fb653bb82128f6cba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9edd29e22f6a7f4d14d9f8d2684d47e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39de1bc04496b97dcf401c669e6ab44e.png)
关于欧拉函数给出下面四个结论:
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bb88141edd6ddf3efbede1cb9b9051.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71b78297a65e7fad69635b19928ecc10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a2eb229ae25851eae3cf941fd46eca4.png)
③若m,n(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7d9712c3b25f3030e166e136d3a4686.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b8178596507fe45cea77096a53d6395.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13ae00da0e4adace07489880ab64d391.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9ef0a61e3c701a7cb3a9f9ca3c8dd37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bced1fbb4e3bde1437f4fb2821d81a9.png)
(注:素数是指除了1和它本身以外不再有其他因数,且大于1的正整数.)
则所有正确结论的序号为
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2 . 设X和Y是两个集合,
且
.证明:
(1)
.
(2)
.
(3)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86d7786f55f767e0a301b5032cdacc79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc6a1190f1f5a16833808df19c437fed.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45e694ec4628362b02045e09923dfdad.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39aaaaa368cbea1c1fa8687da0d43d20.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84cd3c495d19893bb8e0ad2d6b0cfba5.png)
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3 . 对于温度的计量,世界上大部分国家使用摄氏温标(
),少数国家使用华氏温标(
),两种温标间有如下对应关系:
根据表格中数值间呈现的规律,给出下列三个推断:
①
对应
;
②
对应
;
③存在某个温度,其摄氏温标的数值等于其华氏温标的数值.
其中所有正确推断的序号是_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de96374212b9a5df820d78d10e7d1291.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2e6f453529f67d47029e676e101fa1.png)
摄氏温标(![]() | … | 0 | 10 | 20 | 30 | 40 | 50 | … |
华氏温标(![]() | … | 32 | 50 | 68 | 86 | 104 | 122 | … |
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c7889f265b1bac6f19624eb93f5dbdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70e84f0752917be8193ae8904597eb93.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b3ee57b9d71d700e78f43ed84d11e86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bce05b7fe7399da4f3b66f05f6bdf8b8.png)
③存在某个温度,其摄氏温标的数值等于其华氏温标的数值.
其中所有正确推断的序号是
您最近一年使用:0次