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在线作业 发表于 2020-5-21 11:22:11

贵州电大2020年春季《初等数论》形成性考核4资料

2020年春季《初等数论》形成性考核4
1.[单选题] 383是素数，<img width="55" height="55" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/a599184f-5e0c-42b9-a154-36d2030ac420/20161025162120887.jpg" />=（   ）
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    A.1
    B.2
    C.3
    D.4
    答:——A——
2.[单选题] 如果同余式x²=a(modp)有解，则成a是模p的（   ）
    A.一次剩余
    B.二次剩余
    C.三次剩余
    D.四次剩余
    答:——B——
3.[单选题] 设p是奇素数，(a,p)=1，则（   ）
    A.<img width="144" height="51" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/3b88a0ab-fd4d-4e33-a8ee-da519d4b6a2b/20161025162521350.jpg" />
    B.<img width="133" height="53" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/3b88a0ab-fd4d-4e33-a8ee-da519d4b6a2b/20161025162531491.jpg" />
    C.<img width="146" height="52" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/3b88a0ab-fd4d-4e33-a8ee-da519d4b6a2b/20161025162541194.jpg" />
    D.<img width="144" height="50" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/3b88a0ab-fd4d-4e33-a8ee-da519d4b6a2b/2016102516255236.jpg" />
    答:——A——
4.[单选题] 如果(a,p)=1，则a是模p的平方剩余的充要条件是（   ）
    A.<img width="127" height="37" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/f12c053e-1c33-4c06-8346-d000bdf5c913/20161025163020642.jpg" />
    B.<img width="116" height="40" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/f12c053e-1c33-4c06-8346-d000bdf5c913/20161025163030486.jpg" />
    C.<img width="120" height="44" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/f12c053e-1c33-4c06-8346-d000bdf5c913/20161025163044729.jpg" />
    D.<img width="116" height="43" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/f12c053e-1c33-4c06-8346-d000bdf5c913/20161025163055524.jpg" />
    答:————
5.[单选题] 设a₁=a₂（modm），则（   ）
    A.<img width="99" height="60" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/53d6b801-67b7-4367-94c2-90307f834fe8/20161025161922606.jpg" />
    B.<img width="97" height="52" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/53d6b801-67b7-4367-94c2-90307f834fe8/20161025161931904.jpg" />
    C.<img width="102" height="60" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/53d6b801-67b7-4367-94c2-90307f834fe8/20161025161941436.jpg" />
    D.不确定
    答:————
6.[单选题] 如果b₁=b₂（modp），则（   ）
    A.<img width="94" height="58" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/bb9b79a4-ee6f-448d-801b-d8a3fd5f3e7d/20161025162250745.jpg" />
    B.<img width="91" height="55" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/bb9b79a4-ee6f-448d-801b-d8a3fd5f3e7d/2016102516231946.jpg" />
    C.<img width="99" height="58" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/bb9b79a4-ee6f-448d-801b-d8a3fd5f3e7d/2016102516231354.jpg" />
    D.不确定
    答:————
7.[单选题] 同余式12x+15=0(mod45)有解，而且解的个数为(   )
    A.0
    B.1
    C.3
    D.5   奥鹏作业答案可以联系QQ 7 612 960 21
    答:————
8.[单选题] 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（   ）
    A.<img width="68" height="59" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/89316df6-625f-44de-8260-5d8eac6b7361/20161025161318838.jpg" />
    B.<img width="63" height="57" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/89316df6-625f-44de-8260-5d8eac6b7361/20161025161331350.jpg" />
    C.<img width="68" height="56" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/89316df6-625f-44de-8260-5d8eac6b7361/20161025161341334.jpg" />
    D.<img width="64" height="57" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/89316df6-625f-44de-8260-5d8eac6b7361/20161025161350741.jpg" />
    答:————
9.[单选题] 在整数中正素数的个数为(    )
    A.有1个
    B.无限多
    C.有限多
    D.不一定
    答:————
10.[单选题] 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（   ）
    A.<img width="98" height="53" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/33dd4c20-72e7-4fca-a7e9-1bf79ee2ffc2/201610251688439.jpg" />
    B.<img width="102" height="55" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/33dd4c20-72e7-4fca-a7e9-1bf79ee2ffc2/2016102516819219.jpg" />
    C.<img width="98" height="52" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/33dd4c20-72e7-4fca-a7e9-1bf79ee2ffc2/2016102516829967.jpg" />
    D.<img width="96" height="40" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/33dd4c20-72e7-4fca-a7e9-1bf79ee2ffc2/201610251684190.jpg" />
    答:————
11.[单选题] 同余式x²=365（mod1847）的解的情况（   ）
    A.有解
    B.无解
    C.不确定
    D.有无理数解
    答:————
12.[单选题] 同余式x²=2(mod41)的解的情况（   ）
    A.无解
    B.有解
    C.有无理数解
    D.不确定
    答:————
13.[单选题] 形如4n-1的数不能写成（ ）个平方数的和
    A.0
    B.1
    C.2
    D.3
    答:————
14.[单选题] 素数17的平方非剩余是（   ）
    A.1，2，3，4，5，6，7，8, 10
    B.1，2，4，8，9，13，15，16
    C.2，4，6，8，10，12，14，16
    D.3，5，6，7，10，11，12，14
    答:————
15.[单选题] 563是素数，<img width="54" height="54" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201610/3d4f2e15-6683-48ca-9344-652e1fd97d83/2016102516153690.jpg" />=（   ）
    A.0
    B.1
    C.2
    D.3
    答:————
16.[判断题] 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" />
    A.√
    B.×
    答:————
17.[判断题] 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.
    A.√
    B.×
    答:————
18.[判断题] 对于同一素数p,二平方非剩余之积为平方剩余.
    A.√
    B.×
    答:————
19.[判断题] 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.
    A.√
    B.×
    答:————
20.[判断题] 形如4m+1的素数可以写成两个平方数的和.
    A.√
    B.×
    答:————
21.[判断题] 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" />
    A.√
    B.×
    答:————
22.[判断题] 同余式x²=5(mod29)有解
    A.√
    B.×
    答:————
23.[判断题] 同余式x²=3(mod11)无解
    A.√
    B.×
    答:————
24.[判断题] 素数17的平方非剩余有8个.
    A.√
    B.×
    答:————
25.[判断题] 假设x=b(modp)是x²=a(modp)的解，则x=-b(modp)是x²=a(modp)的解
    A.√
    B.×
    答:————

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