名校
1 . 设a,b为非负整数,m为正整数,若a和b被m除得的余数相同,则称a和b对模m同余,记为
.
(1)求证:
;
(2)若p是素数,n为不能被p整除的正整数,则
,这个定理称之为费马小定理.应用费马小定理解决下列问题:
①证明:对于任意整数x都有
;
②求方程
的正整数解的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73aeb67aa5fa6797d0a68cfbf1a3d5.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbfac455432b5ddc11bbbb62b165f1ef.png)
(2)若p是素数,n为不能被p整除的正整数,则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64b82d58ea4cb94ff8dc3aeb1c345a0e.png)
①证明:对于任意整数x都有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/366bfef60e3b2c6fd95003cddbd66605.png)
②求方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bc16a57919b711a9d34eed86b437f35.png)
您最近一年使用:0次
2024-02-27更新
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817次组卷
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5卷引用:河北省秦皇岛市昌黎县开学联考2024届高三下学期开学考试数学试题
河北省秦皇岛市昌黎县开学联考2024届高三下学期开学考试数学试题河北省2024届高三下学期大数据应用调研联合测评(V)数学试题河北省沧州市泊头市大数据联考2024届高三下学期2月月考数学试题(已下线)压轴题高等数学背景下新定义题(九省联考第19题模式)讲(已下线)新题型02 新高考新结构竞赛题型十五大考点汇总-2
名校
解题方法
2 . 已知双曲线
为双曲线
的右焦点,过
作直线
交双曲线
于
两点,过
点且与直线
垂直的直线
交直线
于
点,直线
交双曲线
于
两点.
(1)若直线
的斜率为
,求
的值;
(2)设直线
的斜率分别为
,且
,记
,试探究
与
满足的方程关系,并将
用
表示出来.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/805d185b590f2d9612c271bde13582b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b650820d7bed48ed67a2869ad8c65ff1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1710916ae846e08a5927dae3ad762342.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c65902e35640cf2c8d4111c36b40145.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ee3e87a46fc97708046c37aa77712db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826a579ab176d706e8b6ca0fdc928f6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc13a607ac0c7f76d252d7cb1bb040fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd1be7a4da06623f5af1e03b63efa6a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc13a607ac0c7f76d252d7cb1bb040fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21d29f1900bd8da958a791dbf2cf5676.png)
您最近一年使用:0次
2023-04-08更新
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1673次组卷
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3卷引用:河北省秦皇岛市第一中学2023届高三二模数学试题