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【贵州电大】[初等数论(省)]形成性测试4阶段性测验
试卷总分:100 得分:100
第1题,383是素数,<img width="55" height="55" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/a599184f-5e0c-42b9-a154-36d2030ac420/20161025162120887.jpg" />=(;; )
1
2
3
4
正确资料:
第2题,如果同余式x<sup>2</sup>=a(modp)有解,则成a是模p的(;; )
一次剩余
二次剩余
三次剩余
四次剩余
正确资料:
第3题,设p是奇素数,(a,p)=1,则(;; )
<img width="144" height="51" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/3b88a0ab-fd4d-4e33-a8ee-da519d4b6a2b/20161025162521350.jpg" />
<img width="133" height="53" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/3b88a0ab-fd4d-4e33-a8ee-da519d4b6a2b/20161025162531491.jpg" />
<img width="146" height="52" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/3b88a0ab-fd4d-4e33-a8ee-da519d4b6a2b/20161025162541194.jpg" />
<img width="144" height="50" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/3b88a0ab-fd4d-4e33-a8ee-da519d4b6a2b/2016102516255236.jpg" />
正确资料:
第4题,如果(a,p)=1,则a是模p的平方剩余的充要条件是(;; )
<img width="127" height="37" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/f12c053e-1c33-4c06-8346-d000bdf5c913/20161025163020642.jpg" />
<img width="116" height="40" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/f12c053e-1c33-4c06-8346-d000bdf5c913/20161025163030486.jpg" />
<img width="120" height="44" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/f12c053e-1c33-4c06-8346-d000bdf5c913/20161025163044729.jpg" />
<img width="116" height="43" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/f12c053e-1c33-4c06-8346-d000bdf5c913/20161025163055524.jpg" />
正确资料:
第5题,设a<sub>1</sub>=a<sub>2</sub>(modm),则(;; )
<img width="99" height="60" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/53d6b801-67b7-4367-94c2-90307f834fe8/20161025161922606.jpg" />
<img width="97" height="52" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/53d6b801-67b7-4367-94c2-90307f834fe8/20161025161931904.jpg" />
<img width="102" height="60" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/53d6b801-67b7-4367-94c2-90307f834fe8/20161025161941436.jpg" />
不确定
正确资料:
第6题,如果b<sub>1</sub>=b<sub>2</sub>(modp),则(;; )
<img width="94" height="58" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/bb9b79a4-ee6f-448d-801b-d8a3fd5f3e7d/20161025162250745.jpg" />
<img width="91" height="55" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/bb9b79a4-ee6f-448d-801b-d8a3fd5f3e7d/2016102516231946.jpg" />
<img width="99" height="58" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/bb9b79a4-ee6f-448d-801b-d8a3fd5f3e7d/2016102516231354.jpg" />
不确定
正确资料:
第7题,同余式12x+15=0(mod45)有解,而且解的个数为(;;;)
0
1
3
5
正确资料:
第8题,同余式x<sup>2</sup>=a(modp<sup>k</sup>),p不整除a,p是奇素数,则同余式有解的充要条件为(;; )
<img width="68" height="59" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/89316df6-625f-44de-8260-5d8eac6b7361/20161025161318838.jpg" />
<img width="63" height="57" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/89316df6-625f-44de-8260-5d8eac6b7361/20161025161331350.jpg" />
<img width="68" height="56" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/89316df6-625f-44de-8260-5d8eac6b7361/20161025161341334.jpg" />
<img width="64" height="57" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/89316df6-625f-44de-8260-5d8eac6b7361/20161025161350741.jpg" />
正确资料:
第9题,在整数中正素数的个数为(;;;;)
有1个
无限多
有限多
不一定
正确资料:
第10题,模p的简化剩余系中平方剩余与平方非剩余的个数分别是(;; )
<img width="98" height="53" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/33dd4c20-72e7-4fca-a7e9-1bf79ee2ffc2/201610251688439.jpg" />
<img width="102" height="55" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/33dd4c20-72e7-4fca-a7e9-1bf79ee2ffc2/2016102516819219.jpg" />
<img width="98" height="52" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/33dd4c20-72e7-4fca-a7e9-1bf79ee2ffc2/2016102516829967.jpg" />
<img width="96" height="40" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/33dd4c20-72e7-4fca-a7e9-1bf79ee2ffc2/201610251684190.jpg" />
正确资料:
第11题,同余式x<sup>2</sup>=365(mod1847)的解的情况(;; )
有解
无解
不确定
有无理数解
正确资料:
第12题,同余式x<sup>2</sup>=2(mod41)的解的情况(;; )
无解
有解
有无理数解
不确定
正确资料:
第13题,形如4n-1的数不能写成(;)个平方数的和
0
1
2
3
正确资料:
第14题,素数17的平方非剩余是(;;;;;)
1,2,3,4,5,6,7,8,;10
1,2,4,8,9,13,15,16
2,4,6,8,10,12,14,16
3,5,6,7,10,11,12,14
正确资料:
第15题,563是素数,<img width="54" height="54" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/3d4f2e15-6683-48ca-9344-652e1fd97d83/2016102516153690.jpg" />=(;; )
0
1
2
3
正确资料:
第16题,如果p,q是奇素数,(p,q)=1,则<img width="162" height="60" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/c9a9f4e3-966c-49a5-b4f9-6f717283e29e/2016102516128884.jpg" />
√
×
正确资料:
第17题,对于同一素数p,一平方剩余与一平方非剩余之积为平方剩余.
√
×
正确资料:
第18题,对于同一素数p,二平方非剩余之积为平方剩余.
√
×
正确资料:
第19题,一个能表成两个平方数和的数与一个平方数的乘积,仍然是两个平方数的和.
√
×
正确资料:
第20题,形如4m+1的素数可以写成两个平方数的和.
√
×
正确资料:
第21题,设p为素数,则<img width="62" height="51" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/728ea949-b462-4032-9f77-f508bb935780/2016102516315169.jpg" />
√
×
正确资料:
第22题,同余式x<sup>2</sup>=5(mod29)有解
√
×
正确资料:
第23题,同余式x<sup>2</sup>=3(mod11)无解
√
×
正确资料:
第24题,素数17的平方非剩余有8个.
√
×
正确资料:
第25题,假设x=b(modp)是x<sup>2</sup>=a(modp)的解,则x=-b(modp)是x<sup>2</sup>=a(modp)的解
√
×
正确资料:
第26题,当p=8k±3时,2是(;;;;)
一次剩余
二次剩余
二次非剩余
不确定
正确资料:
第27题,同余式x<sup>2</sup>=57(mod64)的解的个数(;; )
3
1
2
4
正确资料:
第28题,同余式3x=1(mod17)的解为(;;;;;)
x=6(mod17)
x=2(mod17)
x=3(mod17)
x=4(mod17)
正确资料:
第29题,11的平方剩余的个数为(;;;;)
5
6
7
8
正确资料:
第30题,11的平方非剩余的个数为(;;;;)
0
2
8
10
正确资料:
第31题,<p>如果a是模p的平方剩余,则同余式x<sup>2</sup>=a(modp)有(;; )个解
1
2
3
4
正确资料:
第32题,17的平方非剩余的个数为(;;;;)
0
2
8
10
正确资料:
第33题,不定方程x<sup>2</sup>+23y=17(;; )
无解
有无穷多解
有限个解
无法确定
正确资料:
第34题,同余式x<sup>2</sup>=5(mod19)有解
√
×
正确资料:
第35题,一个数如果能写成两个平方数的和,则表示方法是惟一的.
√
×
正确资料:
第36题,两个能表成两个平方数和的数的乘积,也是一个两个平方数和的数.
√
×
正确资料:
第37题,<p>同余式x<sup>2</sup>=438(mod593)(;; )
有解
无解
不确定
有小数解
正确资料:
第38题,<p>设m,n是大于的奇数,且(a,mn)=1,则(;; )
<img width="130" height="51" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/bed226ec-55d6-49a9-989b-9b0c76aa72dc/201610251617311.jpg" />
<img width="130" height="55" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/bed226ec-55d6-49a9-989b-9b0c76aa72dc/20161025161741110.jpg" />
<img width="93" height="48" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/bed226ec-55d6-49a9-989b-9b0c76aa72dc/20161025161750923.jpg" />
不确定
正确资料:
第39题,17的平方剩余的个数为(;;;;)
5
6
7
8
正确资料:
第40题,如果(a,p)=1,则a是模p的平方非剩余的充要条件是(;; )
<img width="113" height="43" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/e72b8c90-c2d6-4f74-a910-741e6da75af7/20161025163228658.jpg" />
<img width="116" height="43" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/e72b8c90-c2d6-4f74-a910-741e6da75af7/20161025163244196.jpg" />
<img width="129" height="43" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/e72b8c90-c2d6-4f74-a910-741e6da75af7/2016102516333151.jpg" />
<img width="117" height="38" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/e72b8c90-c2d6-4f74-a910-741e6da75af7/20161025163312526.jpg" />
正确资料:
第41题,当p=8k±1时,2是(;;;;)
一次剩余
二次剩余
二次非剩余
不确定
正确资料:
第42题,素数写成两个平方数和的方法不是惟一的.
√
×
正确资料:
第43题,素数17的平方剩余有16个.
√
×
正确资料:
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