名校
解题方法
1 . 数列
满足
则称数列
为下凸数列.
(1)证明:任意一个正项等比数列均为下凸数列;
(2)设
,其中
,
分别是公比为
,
的两个正项等比数列,且
,证明:
是下凸数列且不是等比数列;
(3)若正项下凸数列的前
项和为
,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0bee75d4d83c0b76421fd87113e4dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)证明:任意一个正项等比数列均为下凸数列;
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f67fc95a626251da11649acb5e1706f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c340d7d093dd4a275ffea4b87cd26827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6268630d5e5288048d32f4aa5c8bc02d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c171ff5c2728e7cf00a88f88de14f308.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3755d7aa870e2f199d6c12264fc9be86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
(3)若正项下凸数列的前
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0002f427eded1721f43d60dd0fd3ffe0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd419dc0a6580ab97777b2cb8fd7cded.png)
您最近一年使用:0次
2024-06-12更新
|
1143次组卷
|
5卷引用:福建省龙岩市上杭县第一中学2024届高三下学期5月数学模拟试题
名校
解题方法
2 . 设
,
.如果存在
使得
,那么就说
可被
整除(或
整除
),记做
且称
是
的倍数,
是
的约数(也可称为除数、因数).
不能被
整除就记做
.由整除的定义,不难得出整除的下面几条性质:①若
,
,则
;②
,
互质,若
,
,则
;③若
,则
,其中
.
(1)若数列
满足,
,其前
项和为
,证明:
;
(2)若
为奇数,求证:
能被
整除;
(3)对于整数
与
,
,求证:
可整除
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b72ea8ec0d9f8b1cfc4de834b8bfb608.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87803b7cee18366b89d51799250df510.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6705dba65746e1d4cac6a268b3c806ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/020e12ff4f028aba3a205a95e650d72b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79bda3d07c2fef4d6af4a13ade4c743e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/020e12ff4f028aba3a205a95e650d72b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e4d6df2a57b7e5be32c05c10257ea6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91638bacbf4d15736d26713ba90e0fc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91638bacbf4d15736d26713ba90e0fc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e4d6df2a57b7e5be32c05c10257ea6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0601879ae4ca9592246d135bfa48658c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383eb235f8e0ceda13367b16d29e0180.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/503618b9bfb53a06f0ec6a5e427dcdbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0da20edf2714109dcfded7e212ec44a.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e12059d1dac926a235ccd40c3b61b1b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed9dbd8ed61db4f1c14f6b0e5f071200.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e1e4de97f8490fddcff16afe8583266.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
(3)对于整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b96cdd9e003120b6102d927dbf53e39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5009ce2d56180d31204f77c871fb375c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4b326965628b5d967aafe9e696fdc07.png)
您最近一年使用:0次
2024-05-19更新
|
539次组卷
|
2卷引用:河南省驻马店市新蔡县第一高级中学2023-2024学年高二下学期6月月考数学试题
3 .
个有次序的实数
所组成的有序数组
称为一个n维向量,其中
称为该向量的第
个分量.特别地,对一个n维向量
,若
,
,称
为n维信号向量.设
,则
和
的内积定义为
,且
.
(1)写出所有3维信号向量;
(2)直接写出4个两两垂直的4维信号向量;
(3)证明:不存在14个两两垂直的14维信号向量;
(4)已知
个两两垂直的2024维信号向量
满足它们的前
个分量都是相同的,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f2b043b989216035c6fd985f1dd6a3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97de4e0337716e1d89eb1a6cfd7b8335.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6e51ca089ee13a138e985e20f1b7b3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c43d0d6f87afa8b4fd5f6cf81f2bdcdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da796531c7b6c590a22b811df1fcef53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/293e6a784d135c77e3bded6f48f6eec9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b6be373930634c9aa53fec30bec8896.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea2978e42bc0f5abe31fe2536969afa9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19c7c807358869b70becd16ca80e1714.png)
(1)写出所有3维信号向量;
(2)直接写出4个两两垂直的4维信号向量;
(3)证明:不存在14个两两垂直的14维信号向量;
(4)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb9cae65660b220cc622b87ed9eea092.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf2182d0dad848ccc76944d976befbf2.png)
您最近一年使用:0次
4 . 已知
为坐标原点,
,
.
(1)判断
的形状,并给予证明;
(2)若
,求证:
、
、
三点共线;
(3)若
是线段
上靠近点
的四等分点,求
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51116e96f4c35d90677e91e0aa914111.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9612a17c77d5d6ded6123e12f9c8914.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4bdb30cad5418d2b634e697d2d8e46e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
您最近一年使用:0次
5 . 设自然数
,由
个不同正整数
构成集合
,若集合
的每一个非空子集所含元素的和构成新的集合
,记
为集合
元素的个数
(1)已知集合
,集合
,分别求解
.
(2)对于集合
,若
取得最大值,则称该集合
为“极异集合”
①求
的最大值(无需证明).
②已知集合
是极异集合,记
求证:数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c23747e7321187323c665a641adb49e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84357e7e15c0b4187ea69a4d555ef171.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e29fd31a1808968790032a671f64be90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9a84d5316c5db87fda9b7d615c9dce6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e29fd31a1808968790032a671f64be90.png)
(1)已知集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ccaf946a034215b8c49c12a1aff7790.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d160c80e7542650f9ac8ff3981548ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11391d21b5da91adc137d57a73c19b83.png)
(2)对于集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84357e7e15c0b4187ea69a4d555ef171.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9a84d5316c5db87fda9b7d615c9dce6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9a84d5316c5db87fda9b7d615c9dce6.png)
②已知集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84357e7e15c0b4187ea69a4d555ef171.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35e9ca7e90d47d7ee295338bbac2d8d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7477e3d7c54f409ee9905e81c9cbe2f.png)
您最近一年使用:0次
解题方法
6 . 如果![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e75cb7615ca33b128496114742a1f2dd.png)
(1)求证:
;
(2)若
为三角形的三个内角,判断
与
的大小关系,并予以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e75cb7615ca33b128496114742a1f2dd.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3e10e76a8cf6e3eb92e57ee971a218a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e263f0291e3df8b6fb866abaf3f4576.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbeb449ec91ac7e5798e3b347fd0d107.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89a25e473dce119ddd92f32fef1dc576.png)
您最近一年使用:0次
名校
解题方法
7 . 若数列
满足
,其中
,则称数列
为M数列.
(1)已知数列
为M数列,当
时.
(ⅰ)求证:数列
是等差数列,并写出数列
的通项公式;
(ⅱ)
,求
.
(2)若
是M数列
,且
,证明:存在正整数n.使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a07614926587f57bc5f341c4f97f4d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec574b71bbd7671223f8c833c8c8b61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ec1a744042c32d0a851f98fafaa81f3.png)
(ⅰ)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/362832fa3d3c13c1eafd565349d66dce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/115da54f93de5e89d1e7f443fccb61f8.png)
(ⅱ)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0992722f5002aeafa39d25c6b5f4644b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21085fbd6c4b34588f17fc466c845ffe.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a789a9be1723bfbd38ae538a9f39dc1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4ce64685821c3e55c07f151996ca8c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/446e8a7985d4d3dd95c70dc4aad67861.png)
您最近一年使用:0次
2024-03-25更新
|
1250次组卷
|
3卷引用:河南省南阳市西峡县第一高级中学2023-2024学年高二下学期第一次月考数学试卷
名校
8 . (1)已知k,
,且
,求证:
;
(2)若
,且
,证明:
;
(3)设数列
,
,
,…,
是公差不为0的等差数列,证明:对任意的
,函数
是关于x的一次函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53b4b3879d1c6debf0333008f686634e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e10e0bb04d7d261d880aea655e19db1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/030d7dbc61a27892cd24b1c4d21745ee.png)
(3)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f35f7dcce39f3d4dc6b7faf84dc1d0a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19dbbfed8a6279c3c233cdd1795946ed.png)
您最近一年使用:0次
名校
9 . 在正项无穷数列
中,若对任意的
,都存在
,使得
,则称
为
阶等比数列.在无穷数列
中,若对任意的
,都存在
,使得
,则称
为
阶等差数列.
(1)若
为1阶等比数列,
,求
的通项公式及前
项和;
(2)若
为
阶等比数列,求证:
为
阶等差数列;
(3)若
既是4阶等比数列,又是5阶等比数列,证明:
是等比数列.
![](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/c7905fd422e78a1d22ff6f11950bc5cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d7f4b6e82924087d9fa4523cd509d06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7905fd422e78a1d22ff6f11950bc5cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41a08caf919ff9fa62e20d91af57c401.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0831836c71efc1b1ffdb73073da2a2dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dc71a2fd8c6b263feea5ff5d6a36121.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
2024-03-10更新
|
955次组卷
|
4卷引用:山东省德州市第一中学2023-2024学年高二下学期3月月考数学试题
名校
10 . 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
|
824次组卷
|
5卷引用: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
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