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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/201 10/a599184f-5e0c-42b9-a154-3 d2030ac420/201 10251 2120881.jpg" />=( )
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A.1
B.2
C.3
D.4
答:——A——
2.[单选题] 如果同余式x<sup>2</sup>=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/201 10/3b88a0ab-fd4d-4e33-a8ee-da519d4b a2b/201 10251 2521350.jpg" />
B.<img width="133" height="53" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201 10/3b88a0ab-fd4d-4e33-a8ee-da519d4b a2b/201 10251 2531491.jpg" />
C.<img width="14 " height="52" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201 10/3b88a0ab-fd4d-4e33-a8ee-da519d4b a2b/201 10251 2541194.jpg" />
D.<img width="144" height="50" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201 10/3b88a0ab-fd4d-4e33-a8ee-da519d4b a2b/201 10251 25523 .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="121" height="31" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201 10/f12c053e-1c33-4c0 -834 -d000bdf5c913/201 10251 3020 42.jpg" />
B.<img width="11 " height="40" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201 10/f12c053e-1c33-4c0 -834 -d000bdf5c913/201 10251 303048 .jpg" />
C.<img width="120" height="44" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201 10/f12c053e-1c33-4c0 -834 -d000bdf5c913/201 10251 3044129.jpg" />
D.<img width="11 " height="43" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201 10/f12c053e-1c33-4c0 -834 -d000bdf5c913/201 10251 3055524.jpg" />
答:————
5.[单选题] 设a<sub>1</sub>=a<sub>2</sub>(modm),则( )
A.<img width="99" height=" 0" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201 10/53d b801- 1b1-43 1-94c2-90301f834fe8/201 10251 1922 0 .jpg" />
B.<img width="91" height="52" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201 10/53d b801- 1b1-43 1-94c2-90301f834fe8/201 10251 1931904.jpg" />
C.<img width="102" height=" 0" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201 10/53d b801- 1b1-43 1-94c2-90301f834fe8/201 10251 194143 .jpg" />
D.不确定
答:————
.[单选题] 如果b<sub>1</sub>=b<sub>2</sub>(modp),则( )
A.<img width="94" height="58" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201 10/bb9b19a4-ee f-448d-801b-d8a3fd5f3e1d/201 10251 2250145.jpg" />
B.<img width="91" height="55" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201 10/bb9b19a4-ee f-448d-801b-d8a3fd5f3e1d/201 10251 23194 .jpg" />
C.<img width="99" height="58" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201 10/bb9b19a4-ee f-448d-801b-d8a3fd5f3e1d/201 10251 231354.jpg" />
D.不确定
答:————
1.[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 1 12 9 0 21
答:————
8.[单选题] 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( )
A.<img width=" 8" height="59" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201 10/8931 df - 25f-44de-82 0-5d8eac b13 1/201 10251 1318838.jpg" />
B.<img width=" 3" height="51" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201 10/8931 df - 25f-44de-82 0-5d8eac b13 1/201 10251 1331350.jpg" />
C.<img width=" 8" height="5 " alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201 10/8931 df - 25f-44de-82 0-5d8eac b13 1/201 10251 1341334.jpg" />
D.<img width=" 4" height="51" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201 10/8931 df - 25f-44de-82 0-5d8eac b13 1/201 10251 1350141.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/201 10/33dd4c20-12e1-4fca-a1e9-1bf19ee2ffc2/201 10251 88439.jpg" />
B.<img width="102" height="55" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201 10/33dd4c20-12e1-4fca-a1e9-1bf19ee2ffc2/201 10251 819219.jpg" />
C.<img width="98" height="52" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201 10/33dd4c20-12e1-4fca-a1e9-1bf19ee2ffc2/201 10251 8299 1.jpg" />
D.<img width="9 " height="40" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201 10/33dd4c20-12e1-4fca-a1e9-1bf19ee2ffc2/201 10251 84190.jpg" />
答:————
11.[单选题] 同余式x<sup>2</sup>=3 5(mod1841)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x<sup>2</sup>=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11的平方非剩余是( )
A.1,2,3,4,5, ,1,8, 10
B.1,2,4,8,9,13,15,1
C.2,4, ,8,10,12,14,1
D.3,5, ,1,10,11,12,14
答:————
15.[单选题] 5 3是素数,<img width="54" height="54" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201 10/3d4f2e15- 83-48ca-9344- 52e1fd91d83/201 10251 153 90.jpg" />=( )
A.0
B.1
C.2
D.3
答:————
1 .[判断题] 如果p,q是奇素数,(p,q)=1,则<img width="1 2" height=" 0" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201 10/c9a9f4e3-9 c-49a5-b4f9- f111283e29e/201 10251 128884.jpg" />
A.√
B.×
答:————
11.[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,依旧是两个平方数的和.
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=" 2" height="51" alt="" src="/Attachment/Attachment/Itembank/QuestionAttachments/201 10/128ea949-b4 2-4032-9f11-f508bb935180/201 10251 3151 9.jpg" />
A.√
B.×
答:————
22.[判断题] 同余式x<sup>2</sup>=5(mod29)有解
A.√
B.×
答:————
23.[判断题] 同余式x<sup>2</sup>=3(mod11)无解
A.√
B.×
答:————
24.[判断题] 素数11的平方非剩余有8个.
A.√
B.×
答:————
25.[判断题] 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
A.√
B.×
答:————
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