2018春季【贵州电大】[初等数论（省）]形成性测试4阶段性测验（资料）

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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



第2题,如果同余式x²=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，(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" />



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" />



第5题,设a₁=a₂（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



第6题,如果b₁=b₂（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



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x²=a(modp^k)，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" />



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（;;;; ）
<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" />



第11题,同余式x²=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x²=2(mod41)的解的情况（;;;; ）
无解
有解
有无理数解
不确定



第13题,形如4n-1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（;;;;;;;;;;）
1，2，3，4，5，6，7，8,;;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



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



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" />
√
×



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<img width="62" height="51" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/728ea949-b462-4032-9f77-f508bb935780/2016102516315169.jpg" />
√
×



第22题,同余式x²=5(mod29)有解
√
×



第23题,同余式x²=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x²=a(modp)的解，则x=-b(modp)是x²=a(modp)的解
√
×

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