贵州电大2018年秋季[初等数论（省）]形成性测试4阶段性测验

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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贵州电大

第1题383是素数，&ltimgwidth=&quot55&quotheight=&quot55&quotalt=&quot&quotsrc=&quot/Attachment/Attachment/Itembank/QuestionAttachments/201610/a599184f5e0c42b9a15436d2030ac420/20161025162120887.jpg&quot/&gt=（）
1
2
3
4
第2题如果同余式x&ltsup&gt2&lt/sup&gt=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
第3题设p是奇素数，(ap)=1，则（）
&ltimgwidth=&quot144&quotheight=&quot51&quotalt=&quot&quotsrc=&quot/Attachment/Attachment/Itembank/QuestionAttachments/201610/3b88a0abfd4d4e33a8eeda519d4b6a2b/20161025162521350.jpg&quot/&gt
&ltimgwidth=&quot133&quotheight=&quot53&quotalt=&quot&quotsrc=&quot/Attachment/Attachment/Itembank/QuestionAttachments/201610/3b88a0abfd4d4e33a8eeda519d4b6a2b/20161025162531491.jpg&quot/&gt
&ltimgwidth=&quot146&quotheight=&quot52&quotalt=&quot&quotsrc=&quot/Attachment/Attachment/Itembank/QuestionAttachments/201610/3b88a0abfd4d4e33a8eeda519d4b6a2b/20161025162541194.jpg&quot/&gt
&ltimgwidth=&quot144&quotheight=&quot50&quotalt=&quot&quotsrc=&quot/Attachment/Attachment/Itembank/QuestionAttachments/201610/3b88a0abfd4d4e33a8eeda519d4b6a2b/2016102516255236.jpg&quot/&gt
第4题如果(ap)=1，则a是模p的平方剩余的充要条件是（）
&ltimgwidth=&quot127&quotheight=&quot37&quotalt=&quot&quotsrc=&quot/Attachment/Attachment/Itembank/QuestionAttachments/201610/f12c053e1c334c068346d000bdf5c913/20161025163020642.jpg&quot/&gt
&ltimgwidth=&quot116&quotheight=&quot40&quotalt=&quot&quotsrc=&quot/Attachment/Attachment/Itembank/QuestionAttachments/201610/f12c053e1c334c068346d000bdf5c913/20161025163030486.jpg&quot/&gt
&ltimgwidth=&quot120&quotheight=&quot44&quotalt=&quot&quotsrc=&quot/Attachment/Attachment/Itembank/QuestionAttachments/201610/f12c053e1c334c068346d000bdf5c913/20161025163044729.jpg&quot/&gt
&ltimgwidth=&quot116&quotheight=&quot43&quotalt=&quot&quotsrc=&quot/Attachment/Attachment/Itembank/QuestionAttachments/201610/f12c053e1c334c068346d000bdf5c913/20161025163055524.jpg&quot/&gt
第5题设a&ltsub&gt1&lt/sub&gt=a&ltsub&gt2&lt/sub&gt（modm），则（）
&ltimgwidth=&quot99&quotheight=&quot60&quotalt=&quot&quotsrc=&quot/Attachment/Attachment/Itembank/QuestionAttachments/201610/53d6b80167b7436794c290307f834fe8/20161025161922606.jpg&quot/&gt
&ltimgwidth=&quot97&quotheight=&quot52&quotalt=&quot&quotsrc=&quot/Attachment/Attachment/Itembank/QuestionAttachments/201610/53d6b80167b7436794c290307f834fe8/20161025161931904.jpg&quot/&gt
&ltimgwidth=&quot102&quotheight=&quot60&quotalt=&quot&quotsrc=&quot/Attachment/Attachment/Itembank/QuestionAttachments/201610/53d6b80167b7436794c290307f834fe8/20161025161941436.jpg&quot/&gt
不确定
第6题如果b&ltsub&gt1&lt/sub&gt=b&ltsub&gt2&lt/sub&gt（modp），则（）
&ltimgwidth=&quot94&quotheight=&quot58&quotalt=&quot&quotsrc=&quot/Attachment/Attachment/Itembank/QuestionAttachments/201610/bb9b79a4ee6f448d801bd8a3fd5f3e7d/20161025162250745.jpg&quot/&gt
&ltimgwidth=&quot91&quotheight=&quot55&quotalt=&quot&quotsrc=&quot/Attachment/Attachment/Itembank/QuestionAttachments/201610/bb9b79a4ee6f448d801bd8a3fd5f3e7d/2016102516231946.jpg&quot/&gt
&ltimgwidth=&quot99&quotheight=&quot58&quotalt=&quot&quotsrc=&quot/Attachment/Attachment/Itembank/QuestionAttachments/201610/bb9b79a4ee6f448d801bd8a3fd5f3e7d/2016102516231354.jpg&quot/&gt
不确定
第7题同余式12x+15=0(mod45)有解，而且解的个数为()
0
1
3
5
第8题同余式x&ltsup&gt2&lt/sup&gt=a(modp&ltsup&gtk&lt/sup&gt)，p不整除a，p是奇素数，则同余式有解的充要条件为（）
&ltimgwidth=&quot68&quotheight=&quot59&quotalt=&quot&quotsrc=&quot/Attachment/Attachment/Itembank/QuestionAttachments/201610/89316df6625f44de82605d8eac6b7361/20161025161318838.jpg&quot/&gt
&ltimgwidth=&quot63&quotheight=&quot57&quotalt=&quot&quotsrc=&quot/Attachment/Attachment/Itembank/QuestionAttachments/201610/89316df6625f44de82605d8eac6b7361/20161025161331350.jpg&quot/&gt
&ltimgwidth=&quot68&quotheight=&quot56&quotalt=&quot&quotsrc=&quot/Attachment/Attachment/Itembank/QuestionAttachments/201610/89316df6625f44de82605d8eac6b7361/20161025161341334.jpg&quot/&gt
&ltimgwidth=&quot64&quotheight=&quot57&quotalt=&quot&quotsrc=&quot/Attachment/Attachment/Itembank/QuestionAttachments/201610/89316df6625f44de82605d8eac6b7361/20161025161350741.jpg&quot/&gt
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
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（）
&ltimgwidth=&quot98&quotheight=&quot53&quotalt=&quot&quotsrc=&quot/Attachment/Attachment/Itembank/QuestionAttachments/201610/33dd4c2072e74fcaa7e91bf79ee2ffc2/201610251688439.jpg&quot/&gt
&ltimgwidth=&quot102&quotheight=&quot55&quotalt=&quot&quotsrc=&quot/Attachment/Attachment/Itembank/QuestionAttachments/201610/33dd4c2072e74fcaa7e91bf79ee2ffc2/2016102516819219.jpg&quot/&gt
&ltimgwidth=&quot98&quotheight=&quot52&quotalt=&quot&quotsrc=&quot/Attachment/Attachment/Itembank/QuestionAttachments/201610/33dd4c2072e74fcaa7e91bf79ee2ffc2/2016102516829967.jpg&quot/&gt
&ltimgwidth=&quot96&quotheight=&quot40&quotalt=&quot&quotsrc=&quot/Attachment/Attachment/Itembank/QuestionAttachments/201610/33dd4c2072e74fcaa7e91bf79ee2ffc2/201610251684190.jpg&quot/&gt
第11题同余式x&ltsup&gt2&lt/sup&gt=365（mod1847）的解的情况（）
有解
无解
不确定
有无理数解
第12题同余式x&ltsup&gt2&lt/sup&gt=2(mod41)的解的情况（）
无解
有解
有无理数解
不确定
第13题形如4n1的数不能写成（）个平方数的和
0
1
2
3
第14题素数17的平方非剩余是（）
1，2，3，4，5，6，7，810
1，2，4，8，9，13，15，16
2，4，6，8，10，12，14，16
3，5，6，7，10，11，12，14
第15题563是素数，&ltimgwidth=&quot54&quotheight=&quot54&quotalt=&quot&quotsrc=&quot/Attachment/Attachment/Itembank/QuestionAttachments/201610/3d4f2e15668348ca9344652e1fd97d83/2016102516153690.jpg&quot/&gt=（）
0
1
2
3
第16题如果pq是奇素数，(pq)=1，则&ltimgwidth=&quot162&quotheight=&quot60&quotalt=&quot&quotsrc=&quot/Attachment/Attachment/Itembank/QuestionAttachments/201610/c9a9f4e3966c49a5b4f96f717283e29e/2016102516128884.jpg&quot/&gt
√
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.
√
第18题对于同一素数p二平方非剩余之积为平方剩余.
√
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.
√
第20题形如4m+1的素数可以写成两个平方数的和.
√
第21题设p为素数，则&ltimgwidth=&quot62&quotheight=&quot51&quotalt=&quot&quotsrc=&quot/Attachment/Attachment/Itembank/QuestionAttachments/201610/728ea949b46240329f77f508bb935780/2016102516315169.jpg&quot/&gt
√
第22题同余式x&ltsup&gt2&lt/sup&gt=5(mod29)有解
√
第23题同余式x&ltsup&gt2&lt/sup&gt=3(mod11)无解
√
第24题素数17的平方非剩余有8个.
√
第25题假设x=b(modp)是x&ltsup&gt2&lt/sup&gt=a(modp)的解，则x=b(modp)是x&ltsup&gt2&lt/sup&gt=a(modp)的解
√

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