秋形成性測試階段性測驗(yàn)

【貴州電大】[初等數(shù)論（?。形成性測試4階段性測驗(yàn)試卷總分:100得分:100第1題,383是素?cái)?shù)，<imgwidth="55"height="55"alt=""src="/Attachment/Attachment/Itembank/QuestionAttachments/10/a599184f-5e0c-42b9-a154-36d2030ac420/7.jpg"/>=（;;）1234第2題,假如同余式x²=a(modp)有解，則成a是模p（;;）一次剩下二次剩下三次剩下四次剩下第3題,設(shè)p是奇素?cái)?shù)，(a,p)=1，則（;;）<imgwidth="144"height="51"alt=""src="/Attachment/Attachment/Itembank/QuestionAttachments/10/3b88a0ab-fd4d-4e33-a8ee-da519d4b6a2b/0.jpg"/><imgwidth="133"height="53"alt=""src="/Attachment/Attachment/Itembank/QuestionAttachments/10/3b88a0ab-fd4d-4e33-a8ee-da519d4b6a2b/1.jpg"/><imgwidth="146"height="52"alt=""src="/Attachment/Attachment/Itembank/QuestionAttachments/10/3b88a0ab-fd4d-4e33-a8ee-da519d4b6a2b/4.jpg"/><imgwidth="144"height="50"alt=""src="/Attachment/Attachment/Itembank/QuestionAttachments/10/3b88a0ab-fd4d-4e33-a8ee-da519d4b6a2b/.jpg"/>第4題,假如(a,p)=1，則a是模p平方剩下充要條件是（;;）<imgwidth="127"height="37"alt=""src="/Attachment/Attachment/Itembank/QuestionAttachments/10/f12c053e-1c33-4c06-8346-d000bdf5c913/2.jpg"/><imgwidth="116"height="40"alt=""src="/Attachment/Attachment/Itembank/QuestionAttachments/10/f12c053e-1c33-4c06-8346-d000bdf5c913/6.jpg"/><imgwidth="120"height="44"alt=""src="/Attachment/Attachment/Itembank/QuestionAttachments/10/f12c053e-1c33-4c06-8346-d000bdf5c913/9.jpg"/><imgwidth="116"height="43"alt=""src="/Attachment/Attachment/Itembank/QuestionAttachments/10/f12c053e-1c33-4c06-8346-d000bdf5c913/4.jpg"/>第5題,設(shè)a₁=a₂（modm），則（;;）<imgwidth="99"height="60"alt=""src="/Attachment/Attachment/Itembank/QuestionAttachments/10/53d6b801-67b7-4367-94c2-90307f834fe8/6.jpg"/><imgwidth="97"height="52"alt=""src="/Attachment/Attachment/Itembank/QuestionAttachments/10/53d6b801-67b7-4367-94c2-90307f834fe8/4.jpg"/><imgwidth="102"height="60"alt=""src="/Attachment/Attachment/Itembank/QuestionAttachments/10/53d6b801-67b7-4367-94c2-90307f834fe8/6.jpg"/>不確定第6題,假如b₁=b₂（modp），則（;;）<imgwidth="94"height="58"alt=""src="/Attachment/Attachment/Itembank/QuestionAttachments/10/bb9b79a4-ee6f-448d-801b-d8a3fd5f3e7d/5.jpg"/><imgwidth="91"height="55"alt=""src="/Attachment/Attachment/Itembank/QuestionAttachments/10/bb9b79a4-ee6f-448d-801b-d8a3fd5f3e7d/.jpg"/><imgwidth="99"height="58"alt=""src="/Attachment/Attachment/Itembank/QuestionAttachments/10/bb9b79a4-ee6f-448d-801b-d8a3fd5f3e7d/.jpg"/>不確定第7題,同余式12x+15=0(mod45)有解，而且解個(gè)數(shù)為(;;;)0135第8題,同余式x²=a(modp^k)，p不整除a，p是奇素?cái)?shù)，則同余式有解充要條件為（;;）<imgwidth="68"height="59"alt=""src="/Attachment/Attachment/Itembank/QuestionAttachments/10/89316df6-625f-44de-8260-5d8eac6b7361/8.jpg"/><imgwidth="63"height="57"alt=""src="/Attachment/Attachment/Itembank/QuestionAttachments/10/89316df6-625f-44de-8260-5d8eac6b7361/0.jpg"/><imgwidth="68"height="56"alt=""src="/Attachment/Attachment/Itembank/QuestionAttachments/10/89316df6-625f-44de-8260-5d8eac6b7361/4.jpg"/><imgwidth="64"height="57"alt=""src="/Attachment/Attachment/Itembank/QuestionAttachments/10/89316df6-625f-44de-8260-5d8eac6b7361/1.jpg"/>第9題,在整數(shù)中正素?cái)?shù)個(gè)數(shù)為(;;;;)有1個(gè)無限多有限多不一定第10題,模p簡化剩下系中平方剩下與平方非剩下個(gè)數(shù)分別是（;;）<imgwidth="98"height="53"alt=""src="/Attachment/Attachment/Itembank/QuestionAttachments/10/33dd4c20-72e7-4fca-a7e9-1bf79ee2ffc2/.jpg"/><imgwidth="102"height="55"alt=""src="/Attachment/Attachment/Itembank/QuestionAttachments/10/33dd4c20-72e7-4fca-a7e9-1bf79ee2ffc2/.jpg"/><imgwidth="98"height="52"alt=""src="/Attachment/Attachment/Itembank/QuestionAttachments/10/33dd4c20-72e7-4fca-a7e9-1bf79ee2ffc2/.jpg"/><imgwidth="96"height="40"alt=""src="/Attachment/Attachment/Itembank/QuestionAttachments/10/33dd4c20-72e7-4fca-a7e9-1bf79ee2ffc2/.jpg"/>第11題,同余式x²=365（mod1847）解情況（;;）有解無解不確定有沒有理數(shù)解第12題,同余式x²=2(mod41)解情況（;;）無解有解有沒有理數(shù)解不確定第13題,形如4n-1數(shù)不能寫成（;）個(gè)平方數(shù)和0123第14題,素?cái)?shù)17平方非剩下是（;;;;;）1，2，3，4，5，6，7，8,;101，2，4，8，9，13，15，162，4，6，8，10，12，14，163，5，6，7，10，11，12，14第15題,563是素?cái)?shù)，<imgwidth="54"height="54"alt=""src="/Attachment/Attachment/Itembank/QuestionAttachments/10/3d4f2e15-6683-48ca-9344-652e1fd97d83/.jpg"/>=（;;）0123第16題,假如p,q是奇素?cái)?shù)，(p,q)=1，則<imgwidth="162"height="60"alt=""src="/Attachment/Attachment/Itembank/QuestionAttachments/10/c9a9f4e3-966c-49a5-b4f9-6f717283e29e/.jpg"/>√×第17題,對于同一素?cái)?shù)p,一平方剩下與一平方非剩下之積為平方剩下.√×第18題,對于同一素?cái)?shù)p,二平方非剩下之積為平方剩下.√×第19題,一個(gè)能表成兩個(gè)平方數(shù)和數(shù)與一個(gè)平方數(shù)乘積，依然是兩個(gè)平方數(shù)和.√×第20題,形如4m+1素?cái)?shù)能夠?qū)懗蓛蓚€(gè)平方數(shù)和.√×第21題,設(shè)p為素?cái)?shù)，則<imgwidth="62"height="51"alt=""src="/Attachment/Attachment/Itembank/QuestionAttachments/10/728ea949-b462-4032-9f77-f508bb935780/.jpg"/>√×第22題,同余式x²=5(mod29)有解√×第23題,同余式x²=3(mod11)無解√×第24題,素?cái)?shù)17平方非剩下有8個(gè).√×第25題,假設(shè)x=b(modp)是x²=a(modp)解，則x=-b(modp)是x²=a(modp)解√×第26題,當(dāng)p=8k±3時(shí)，2是（;;;;）一次剩下二次剩下二次非剩下不確定第27題,同余式x²=57（mod64）解個(gè)數(shù)（;;）3124第28題,同余式3x=1(mod17)解為（;;;;;）x=6(mod17)x=2(mod17)x=3(mod17)x=4(mod17)第29題,11平方剩下個(gè)數(shù)為（;;;;）5678第