《初等数论》20秋福师模拟题题目

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《初等数论》考前练兵
1.[单选题] 设a,b,c是正整数,则(      )
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    A.<img id="ODzllzaTEMP20200804110950364.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODzllzaTEMP20200804110950364.png?Expires=1911870590&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=v1clbeihS25Qw5u/0dRP69SXZhw%3D" />
    B.<img id="ODcolezTEMP20200804110950719.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODcolezTEMP20200804110950719.png?Expires=1911870590&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=FzUcheOAPXQSwirnMij%2B4Mkmt5g%3D" />
    C.<img id="ODdyuqcTEMP20200804110950939.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODdyuqcTEMP20200804110950939.png?Expires=1911870591&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=zFVCaG92V2QY7uBLFa6upcp6uvM%3D" />
    D.<img id="ODrmeanTEMP20200804110951091.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODrmeanTEMP20200804110951091.png?Expires=1911870591&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=RmbQgVf3Xei9bHKOb13IleckrH4%3D" />
    答:——A——
2.[单选题] 设k是正奇数,则(        )
    A.1 ? 2 ? ? ? 8?1k ? 2k ? ? ? 8k
    B.1 ? 2 ? ? ? 9?1k ? 2k ? ? ? 9k
    C.1 ? 2 ? ? ? 7?1k ? 2k ? ? ? 7k
    D.1 ? 2 ? ? ? 5?1k ? 2k ? ? ? 5k
    答:——B——
3.[单选题] 用辗转相除法求整数x,y,使得1387x ? 162y = (1387, 162),则(      )
    A.<img id="ODmvtnuTEMP20200804110951347.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODmvtnuTEMP20200804110951347.png?Expires=1911870591&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=bsSFJs/7I5%2B8tg7nIcll4jZ9MZg%3D" />
    B.<img id="ODqrwqzTEMP20200804110951499.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODqrwqzTEMP20200804110951499.png?Expires=1911870591&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=wQ%2BvrXeHEKOY5tua4rLm30R3YfY%3D" />
    C.<img id="ODkolzkTEMP20200804110951647.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODkolzkTEMP20200804110951647.png?Expires=1911870591&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=MsWca4VZWHjIS4Yofi7zkwOB6q4%3D" />
    D.<img id="ODttxneTEMP20200804110951791.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODttxneTEMP20200804110951791.png?Expires=1911870592&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=ox8CuWlz6CsRlxBo1dJAOgUE5SA%3D" />
    答:——C——
4.[单选题] <img id="ODmqeuvTEMP20200804110952087.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODmqeuvTEMP20200804110952087.png?Expires=1911870592&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=pCfZTDi3fRcHuFAYs%2BmQzAmQW2E%3D" />(        )
    A.774
    B.516
    C.1032
    D.258
    答:————
5.[单选题] 两整数<img id="ODmyyibTEMP20200804110952269.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODmyyibTEMP20200804110952269.png?Expires=1911870592&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=cPXjvpJXh5fLgntruvTbv1GjqFs%3D" />互质的充分与必要条件是(        )
    A.存在两个整数s,t满足条件<img id="ODaodnmTEMP20200804110952436.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODaodnmTEMP20200804110952436.png?Expires=1911870592&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=24U2c048fkk7u0LC7vyeY61I0z0%3D" />
    B.对任意两个整数s,t满足条件<img id="ODvxpjjTEMP20200804110952605.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODvxpjjTEMP20200804110952605.png?Expires=1911870592&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=XI9ttXDon6HKCSFWkI%2B%2BCpUP6jY%3D" />
    C.存在两个正整数s,t满足条件<img id="ODsahecTEMP20200804110952752.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODsahecTEMP20200804110952752.png?Expires=1911870592&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=PTk0B2DxYl/Wc%2BJ5MZxl/bEk3mA%3D" />
    D.对任意两个正整数s,t满足条件<img id="ODlizlyTEMP20200804110952914.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODlizlyTEMP20200804110952914.png?Expires=1911870593&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=OkPGVZhSi9B1FmITZ/sIPBmj6ak%3D" />
    答:————
6.[单选题] 设<img id="ODsuuxrTEMP20200804110953085.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODsuuxrTEMP20200804110953085.png?Expires=1911870593&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=HpWoW7HPqGmsrHGmFkJ23K1wz44%3D" />,且<img id="ODpiotlTEMP20200804110953237.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODpiotlTEMP20200804110953237.png?Expires=1911870593&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=o/uV3pKC%2BlGG9iFccFwfPqniNgc%3D" />是奇数,则(       )
    A.<img id="ODpjgxxTEMP20200804110953410.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODpjgxxTEMP20200804110953410.png?Expires=1911870593&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=xHoX3fVtyK9NasAjc1FclPP6l4g%3D" />
    B.<img id="ODciwrzTEMP20200804110953579.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODciwrzTEMP20200804110953579.png?Expires=1911870593&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=oe6CgAkm4bnvZgXKbGFvza1m6kQ%3D" />.
    C.<img id="ODyrzzjTEMP20200804110953756.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODyrzzjTEMP20200804110953756.png?Expires=1911870593&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=ZAKWZgIOLWQJX/8tk0OcDd/Y%2B84%3D" />
    D.<img id="ODyafkcTEMP20200804110953915.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODyafkcTEMP20200804110953915.png?Expires=1911870594&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=o9X9ht4gHmPpgwe2I%2B08g8j1qT4%3D" />
    答:————
7.[单选题] 若<img id="ODiugqlTEMP20200804110954082.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODiugqlTEMP20200804110954082.png?Expires=1911870594&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=X5mBMYXZWqpIpMuq4GHk3iAH6wI%3D" />是素数,且<img id="ODwsosoTEMP20200804110954228.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODwsosoTEMP20200804110954228.png?Expires=1911870594&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=2TqlGZyb33Wcoi8d/ap7oAgs5zE%3D" />不能整除<img id="ODpnqqvTEMP20200804110954390.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODpnqqvTEMP20200804110954390.png?Expires=1911870594&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=h5f2Zm8IR2vOg4KIhHcWZ2JjcnU%3D" />,<img id="ODjpwknTEMP20200804110954556.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODjpwknTEMP20200804110954556.png?Expires=1911870594&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=Z/mpF4DfemfTPfyMV7jaJPaMFt8%3D" />,则(         )
    A.<img id="ODgidbtTEMP20200804110954697.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODgidbtTEMP20200804110954697.png?Expires=1911870594&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=cdMJ%2B35NK4asEQiX9tBSQSY5w2Q%3D" />
    B.<img id="ODsmmleTEMP20200804110954857.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODsmmleTEMP20200804110954857.png?Expires=1911870594&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=0PGrfKPZ2Uaa90B8QizOFqTEZ/U%3D" />
    C.<img id="ODqgbkdTEMP20200804110955008.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODqgbkdTEMP20200804110955008.png?Expires=1911870595&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=CEQblKXiyAbbTraMV81OxsEiXho%3D" />
    D.<img id="ODqivgkTEMP20200804110955169.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODqivgkTEMP20200804110955169.png?Expires=1911870595&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=43Rh1WE6RPeH6w8ufu199d4l%2BSo%3D" />
    答:————
8.[单选题] 若2n ? 1是素数,则n是(         )
    A.<img id="ODfathoTEMP20200804110955352.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODfathoTEMP20200804110955352.png?Expires=1911870595&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=kmJxSlEhtkUrhCpj/%2BsljKlB16Y%3D" />
    B.<img id="ODksrfxTEMP20200804110955493.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODksrfxTEMP20200804110955493.png?Expires=1911870595&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=K3nIFf4bihTwspNtSDm4kfRXSJI%3D" />
    C.合数
    D.素数
    答:————
9.[单选题] 以下结论正确的是(       )
    A.<img id="ODooqooTEMP20200804110955653.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODooqooTEMP20200804110955653.png?Expires=1911870595&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=Hrt/gEsDm7HDMN3omL1k4ZNVftw%3D" />
    B.<img id="ODclflsTEMP20200804110955817.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODclflsTEMP20200804110955817.png?Expires=1911870595&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=4OchMqnU1LHq0QV394JZZk0zAg4%3D" />
    C.<img id="ODhtulcTEMP20200804110955975.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODhtulcTEMP20200804110955975.png?Expires=1911870596&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=bYAXr6NKILmd4xxukJXCtWLwE3U%3D" />
    D.<img id="ODdymxrTEMP20200804110956125.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODdymxrTEMP20200804110956125.png?Expires=1911870596&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=7q9F1orQH6KqeySsvvISYh0hMq0%3D" />
    答:————
10.[单选题] 设<img id="ODaqzcvTEMP20200804110956303.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODaqzcvTEMP20200804110956303.png?Expires=1911870596&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=kkuflqw3MeX1YmtmZkOlJiJwIjQ%3D" />都是实数,则(       )
    A.<img id="ODbmzkkTEMP20200804110956467.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODbmzkkTEMP20200804110956467.png?Expires=1911870596&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=yDctbuMJVXvotCAFleFkuntXKMg%3D" />
    B.<img id="ODruqolTEMP20200804110956654.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODruqolTEMP20200804110956654.png?Expires=1911870596&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=NTlckgHTpfYbmmsCdmuH4S4DNlU%3D" />
    C.<img id="ODgiwusTEMP20200804110956847.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODgiwusTEMP20200804110956847.png?Expires=1911870597&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=CMK9lfhYaqfqA34H/SbShOzTLbc%3D" />
    D.<img id="ODaxcnvTEMP20200804110957062.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODaxcnvTEMP20200804110957062.png?Expires=1911870597&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=zIjKW4nN1wjj%2BJ2odTutQZ9sOPQ%3D" />
    答:————
11.[单选题] 313159被7除的余数等于(       )
    A.4
    B.5
    C.6
    D.7
    答:————
12.[单选题] 设<img id="ODcitzaTEMP20200804110957219.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODcitzaTEMP20200804110957219.png?Expires=1911870597&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=67QvdWsW6dB0zNZMPoRVgCf6zhw%3D" />是整系数多项式,且<img id="ODiqhhvTEMP20200804110957612.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODiqhhvTEMP20200804110957612.png?Expires=1911870597&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=z6Hyi6ggqLLAO9afVk8vJsdgGOY%3D" />都不能被<img id="ODjdzhrTEMP20200804110957764.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODjdzhrTEMP20200804110957764.png?Expires=1911870597&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=m/3YGYqJQorCwJLvZ53C1f82q4U%3D" />整除,则(       )
    A.方程<img id="ODdkxwbTEMP20200804110957942.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODdkxwbTEMP20200804110957942.png?Expires=1911870598&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=7wE%2B5h94UbtCk67yBIsGkXppr%2BQ%3D" />只有零解
    B.方程<img id="ODtapekTEMP20200804110958113.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODtapekTEMP20200804110958113.png?Expires=1911870598&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=lVZfspmknkR6OguuS0aRMdRZOug%3D" />有正整数解
    C.方程<img id="ODwnnzbTEMP20200804110958269.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODwnnzbTEMP20200804110958269.png?Expires=1911870598&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=n9O%2B0Y7hGoc7ua9omzUPxp0vmWE%3D" />有负整数解
    D.方程<img id="ODesztqTEMP20200804110958450.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODesztqTEMP20200804110958450.png?Expires=1911870598&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=EIwOcd6V0TBLWPjEOyBYNK5/c4U%3D" />没有整数解
    答:————
13.[单选题] <img id="ODgvnvjTEMP20200804110958597.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODgvnvjTEMP20200804110958597.png?Expires=1911870598&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=qtggGEgloIgLITqNVsNA/Vr5awg%3D" />的个位数字是(      )
    A.3
    B.4
    C.5
    D.6
    答:————
14.[单选题] 以下结论正确的是(     )
    A.若<img id="ODgnzbvTEMP20200804110958748.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODgnzbvTEMP20200804110958748.png?Expires=1911870598&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=x8QTe61UnrYxOrjc71y0h89hOyQ%3D" />都是<img id="ODvlfasTEMP20200804110958903.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODvlfasTEMP20200804110958903.png?Expires=1911870599&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=KJXfIPHLUn%2BpAMZ2sjGK/Ip71CI%3D" />的倍数,<img id="ODavofhTEMP20200804110959071.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODavofhTEMP20200804110959071.png?Expires=1911870599&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=8fk2gNJqbU0TJR5dvDNpdZJO2gU%3D" />任意<img id="ODxjtubTEMP20200804110959230.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODxjtubTEMP20200804110959230.png?Expires=1911870599&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=AepSVdtLp0/6Xz827ZL7VgN2V4c%3D" />个整数,则<img id="ODwjggoTEMP20200804110959527.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODwjggoTEMP20200804110959527.png?Expires=1911870599&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=uRgSsMnF2poknYLSCiLT2sBe0SE%3D" />是<img id="ODyebdaTEMP20200804110959672.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODyebdaTEMP20200804110959672.png?Expires=1911870599&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=P3mAv/iEBLlnURtwtOpHncf6UCo%3D" />的倍数.
    B.若m ? p?mn ? pq,则m ? p?mq
    C.若m ? p?mn ? pq,则m ? p?np
    D.若<img id="ODhgljyTEMP20200804110959856.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODhgljyTEMP20200804110959856.png?Expires=1911870600&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=HvvutBbKBfADXFPOmaNrMUY76KQ%3D" />,则对任意<img id="ODypnnwTEMP20200804111000041.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODypnnwTEMP20200804111000041.png?Expires=1911870600&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=vElvCNNUACk%2BMYYth/5p0KyabNw%3D" />,<img id="ODkztftTEMP20200804111000214.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODkztftTEMP20200804111000214.png?Expires=1911870600&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=trH8i%2BUSfVZmNaU00k9Jes53YAk%3D" />
    答:————
15.[单选题] 以下结论正确的是(      )
    A.若<img id="ODqyczxTEMP20200804111000349.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODqyczxTEMP20200804111000349.png?Expires=1911870600&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=53H3IRMNrj50IEWjsp/EndJ2OkE%3D" />,则<img id="ODfgppvTEMP20200804111000509.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODfgppvTEMP20200804111000509.png?Expires=1911870600&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=pu3Ee/n9kYpjxptivR2KVYMvvy0%3D" />
    B.若<img id="ODehiomTEMP20200804111000673.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODehiomTEMP20200804111000673.png?Expires=1911870600&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=qN8JHXKTYM5tkAN4iPoqhHE3DIg%3D" />,且<img id="ODfmddtTEMP20200804111000829.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODfmddtTEMP20200804111000829.png?Expires=1911870600&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=qxGt0kSlER0zOzaZkv1OAeA3CVc%3D" />,则<img id="ODzgaskTEMP20200804111000968.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODzgaskTEMP20200804111000968.png?Expires=1911870601&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=G12UG9ty8AVa0KazOXoiGQPx6Aw%3D" />
    C.若<img id="ODfqqkqTEMP20200804111001157.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODfqqkqTEMP20200804111001157.png?Expires=1911870601&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=i35%2BrJk05XdZvcnthVUjiMYPAjQ%3D" />,且<img id="ODuwqqnTEMP20200804111001330.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODuwqqnTEMP20200804111001330.png?Expires=1911870601&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=81M9HHJ4CqUzSVVznF35pPEvEAM%3D" />,则<img id="ODyffcdTEMP20200804111001480.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODyffcdTEMP20200804111001480.png?Expires=1911870601&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=JgNsaVJ4Jot8O0a8DO6XYnTpn8U%3D" />
    D.若<img id="ODxudefTEMP20200804111001637.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODxudefTEMP20200804111001637.png?Expires=1911870601&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=k0ZbUR1H/qp8raBqgH6MbYJYBKE%3D" />,且<img id="ODwiajaTEMP20200804111001793.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODwiajaTEMP20200804111001793.png?Expires=1911870601&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=a2zQe4wJclU0BTAdel86RUiCtzs%3D" />,则<img id="ODnolgjTEMP20200804111001953.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODnolgjTEMP20200804111001953.png?Expires=1911870602&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=PBL1h%2BQwGi6Lkgf6XH/WuxkBCww%3D" />
    答:————
16.[单选题] 若 <img id="ODzilkbTEMP20200804111002123.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODzilkbTEMP20200804111002123.png?Expires=1911870602&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=9ChGDQryjCuzwF7tdZS/U0ZKn2k%3D" />且<img id="ODytspaTEMP20200804111002278.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODytspaTEMP20200804111002278.png?Expires=1911870602&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=k6e3VbnPfncCLOXjDjjZkWRlui8%3D" />,则(      )
    A.<img id="ODvsmzaTEMP20200804111002457.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODvsmzaTEMP20200804111002457.png?Expires=1911870602&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=/FuJDurufd3UM5/lsVur5DaD94o%3D" />
    B.<img id="ODbvfbvTEMP20200804111002627.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODbvfbvTEMP20200804111002627.png?Expires=1911870602&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=N2VN%2BVqeBxFfNZ1YKzzB9cf1aHA%3D" />
    C.<img id="ODlucawTEMP20200804111002788.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODlucawTEMP20200804111002788.png?Expires=1911870602&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=9HI5%2B/677BTd5/hp%2B7eHnbbrbuI%3D" />
    D.<img id="ODdgnkhTEMP20200804111002958.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODdgnkhTEMP20200804111002958.png?Expires=1911870603&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=PXmL0LwGezuV1%2Ba%2BeM6apVTs6z0%3D" />
    答:————
17.[单选题] 设正整数<img id="ODvtnxrTEMP20200804111003129.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODvtnxrTEMP20200804111003129.png?Expires=1911870603&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=/J4FtCWXNtfLAYlB1FhUo4ilQbs%3D" />的十进制表示为<img id="ODwznqcTEMP20200804111003278.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODwznqcTEMP20200804111003278.png?Expires=1911870603&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=besFcOMengM3s5M0gic5Zk/WEeU%3D" />,其中<img id="ODlnxgqTEMP20200804111003423.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODlnxgqTEMP20200804111003423.png?Expires=1911870603&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=yM1s7RY%2BIo5fDZiepxPKkYFgcWc%3D" />,且<br><img id="ODcfnraTEMP20200804111003613.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODcfnraTEMP20200804111003613.png?Expires=1911870603&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=25Uqf%2BsjxVk0YvIckVbIOw6XNZY%3D" />,则(    )
    A.<img id="ODoammtTEMP20200804111003793.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODoammtTEMP20200804111003793.png?Expires=1911870603&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=LTtAqX5TaOyxt2t3T0fdfyACxDg%3D" />的充分必要条件是<img id="ODadhmyTEMP20200804111003986.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODadhmyTEMP20200804111003986.png?Expires=1911870604&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=X8Zqkfac3KWYyjZhZTn2NyjESQA%3D" />
    B.<img id="ODmwjtbTEMP20200804111004162.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODmwjtbTEMP20200804111004162.png?Expires=1911870604&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=G5lVkcetxrfXRatGO52QNjNL7rE%3D" />的充分必要条件是<img id="ODfaspnTEMP20200804111004306.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODfaspnTEMP20200804111004306.png?Expires=1911870604&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=nMvAyHoJOqepJX3%2Bio/ehcAiEMo%3D" />
    C.<img id="ODkuncaTEMP20200804111004460.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODkuncaTEMP20200804111004460.png?Expires=1911870604&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=7hTBGo7i4JfaKgPGAMaEDwg3mkE%3D" />的充分必要条件是<img id="ODqxybxTEMP20200804111004617.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODqxybxTEMP20200804111004617.png?Expires=1911870604&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=RE4gjShlWuH6MrA5DJom7N6KC%2BA%3D" />
    D.<img id="ODsncpgTEMP20200804111004806.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODsncpgTEMP20200804111004806.png?Expires=1911870604&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=xFdT8Sa6mcX/xaHHVBhbvRyRYgQ%3D" />的充分必要条件是<img id="ODrfxyiTEMP20200804111004976.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODrfxyiTEMP20200804111004976.png?Expires=1911870605&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=5nTBMiBXYCtjTcdNRWZALRmPSeI%3D" />
    答:————
18.[单选题] 若<img id="ODfedswTEMP20200804111005140.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODfedswTEMP20200804111005140.png?Expires=1911870605&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=gi/CtKu61YQFnaeKepYwR3uRWjA%3D" />是奇数,则(    )
    A.<img id="ODietctTEMP20200804111005339.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODietctTEMP20200804111005339.png?Expires=1911870605&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=K6mOcoafdJwsF4PMez06eCxJJ%2BU%3D" />
    B.<img id="ODrszusTEMP20200804111005500.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODrszusTEMP20200804111005500.png?Expires=1911870605&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=gyJtEwOpxQVNsEfHVis53RAf9b0%3D" />
    C.<img id="ODyoovjTEMP20200804111005654.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODyoovjTEMP20200804111005654.png?Expires=1911870605&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=2bE8iwlfIB0fyXd6WY1qBAmUm0s%3D" />
    D.<img id="ODnwvfuTEMP20200804111005819.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODnwvfuTEMP20200804111005819.png?Expires=1911870605&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=pHdA9XoS3wlqsfz1PZGzIeJip3A%3D" />
    答:————
19.[单选题] 以下结论正确的是(        )
    A.3不能整除<img id="ODcfbdpTEMP20200804111005993.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODcfbdpTEMP20200804111005993.png?Expires=1911870606&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=uQF64SAS5aiYm14gbvlSmH3ERq0%3D" />,n?Z
    B.12?n4 ? 2n3 ? 11n2 ? 10n,n?Z
    C.若3?a2 ? b2,则3不能整除a
    D.若3?a2 ? b2,则3不能整除b
    答:————
20.[单选题] 设x,y?Z,17?2x ? 3y,则(        )
    A.17?9x ? 5y
    B.17?2x
    C.17?3y
    D.17?9x
    答:————
21.[单选题] 以下结论正确的是(     )
    A.<img id="ODktmvqTEMP20200804111006156.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODktmvqTEMP20200804111006156.png?Expires=1911870606&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=U0LFbpD0gE4WU40X6Ue45EiuU1o%3D" />与<img id="ODebaiyTEMP20200804111006329.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODebaiyTEMP20200804111006329.png?Expires=1911870606&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=M/8zqBsadvdk4J7D/i4uaPTQzcE%3D" />有相同的最大公约数
    B.<img id="ODzrihiTEMP20200804111006493.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODzrihiTEMP20200804111006493.png?Expires=1911870606&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=OxoAo9DQbY9GLHjHZl3y97ICsH0%3D" />与<img id="ODryopjTEMP20200804111006656.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODryopjTEMP20200804111006656.png?Expires=1911870606&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=whjbYxM80pg5mMuUZWVD8xJP9zk%3D" />的最大公约数不相等
    C.<img id="ODoxzbcTEMP20200804111006832.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODoxzbcTEMP20200804111006832.png?Expires=1911870606&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=W/5aJS2rP/%2BgfwTTbJlWNlodTyM%3D" />与<img id="ODiecqoTEMP20200804111006989.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODiecqoTEMP20200804111006989.png?Expires=1911870607&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=CdpheHGOV5nBAVN20puqa6w0fF0%3D" />的最小公倍数不相等
    D.设<img id="ODppacaTEMP20200804111007151.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODppacaTEMP20200804111007151.png?Expires=1911870607&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=PFvQXhndc/ujmORCMI7umc9gaoE%3D" />是<img id="ODzmdjyTEMP20200804111007313.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODzmdjyTEMP20200804111007313.png?Expires=1911870607&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=3lXtcahL2mVxFYZnAI%2BwEUnsGpA%3D" />的任意一个公倍数,则<img id="ODfltooTEMP20200804111007498.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODfltooTEMP20200804111007498.png?Expires=1911870607&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=J8OKuDON6IJEZQxV%2Bg7CTv6sr5w%3D" />
    答:————
22.[单选题] 设a,b,c?N,c无平方因子,a2?b2c,则(      )
    A.b?a
    B.a?b
    C.a?c
    D.c?a
    答:————
23.[单选题] 设a,b是正整数,则(       )
    A.(a ? b)[a, b] =b[b, a ? b]
    B.(a ? b)[a, b] = a[b, a - b]
    C.(a ? b)[a, b] = a[b, a ? b]
    D.(a - b)[a, b] = a[b, a - b]
    答:————
24.[单选题] 设a,b是正整数,且a < b,使得a ? b = 120,(a, b) = 24,[a, b] = 144,则(    )
    A.<img id="ODmsgazTEMP20200804111007675.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODmsgazTEMP20200804111007675.png?Expires=1911870607&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=LGTcyRXDQ%2BJyH4bEfIvJmy4S6Lc%3D" />
    B.<img id="ODqhcuyTEMP20200804111007845.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODqhcuyTEMP20200804111007845.png?Expires=1911870607&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=YY%2BM3rnuUhyns7gKbbYRBDNbEdw%3D" />
    C.<img id="ODvlxbxTEMP20200804111007993.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODvlxbxTEMP20200804111007993.png?Expires=1911870608&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=sUVAiln6NaK0JYExiAg0h%2BYNzUg%3D" />
    D.<img id="ODtweswTEMP20200804111008136.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODtweswTEMP20200804111008136.png?Expires=1911870608&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=bMZd94pEtrqm5ja3GWcM73CEQPM%3D" />
    答:————
25.[单选题] 设<img id="ODxflxpTEMP20200804111008291.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODxflxpTEMP20200804111008291.png?Expires=1911870608&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=Yu8lQs8LoDmYZz54j03aZhvHhgs%3D" />为正整数,则(     )
    A.<img id="ODdjcrzTEMP20200804111008467.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODdjcrzTEMP20200804111008467.png?Expires=1911870608&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=Xq5XUdTy%2BoRDhalzjSc8rY7l7LA%3D" />
    B.<img id="ODrnkfbTEMP20200804111008660.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODrnkfbTEMP20200804111008660.png?Expires=1911870608&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=nRp8z%2BdQ%2B4p6hUTeIQlhqckWryw%3D" />
    C.<img id="ODrpgflTEMP20200804111008836.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODrpgflTEMP20200804111008836.png?Expires=1911870608&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=mtfFsGS9lnrDT2fmoQREdj13Cs4%3D" />
    D.<img id="ODyyujsTEMP20200804111008984.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODyyujsTEMP20200804111008984.png?Expires=1911870609&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=WRntSLQ2sWhOutn9geds%2BVLvvzw%3D" />
    答:————
26.[单选题] 设<img id="ODdjvqqTEMP20200804111009159.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODdjvqqTEMP20200804111009159.png?Expires=1911870609&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=BSsvE2hgw5dCe3Nhywdw4hYIg1k%3D" />为正整数,则(     )
    A.<img id="ODvcqxlTEMP20200804111009312.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODvcqxlTEMP20200804111009312.png?Expires=1911870609&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=tbYjTvSKCETo4lWn0DpJzwf07Y0%3D" />
    B.<img id="ODkjcbxTEMP20200804111009481.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODkjcbxTEMP20200804111009481.png?Expires=1911870609&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=lUpBFgReD%2BLZYi9mvb4XQHOFM2s%3D" />
    C.<img id="ODxeoegTEMP20200804111009644.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODxeoegTEMP20200804111009644.png?Expires=1911870609&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=jzY161VksbE4uncg6eQSnrSbvoU%3D" />
    D.<img id="ODmhweeTEMP20200804111009798.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0804/ODmhweeTEMP20200804111009798.png?Expires=1911870609&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=LhPYQGsgJiFf0SNlV6cTL%2BTj1Tk%3D" />
    答:————
27.[问答题] 简述模m的完全剩余系的特征,并给出模m的完全剩余系的一个充分必要条件,其中m为正整数.
    答:————
28.[问答题] 叙述最大公因数和最小公倍数的定义,并简述二者的联系.
    答:————
29.[问答题] 叙述不定方程的定义,并简述n元一次不定方程的一般解的求法.
    答:————
30.[问答题] 简述欧拉定理和Wilson定理的证明过程中蕴涵的数学思想方法.
    答:————
31.[问答题] 判定 (ⅰ)  2x3 ? x2 ? 3x ? 1 ? 0 (mod 5)是否有三个解;(ⅱ)  x6 ? 2x5 ? 4x2 ? 3 ? 0 (mod 5)是否有六个解?
    答:————
32.[问答题] 解同余方程:3x2?11x?20 ? 0 (mod 105)。
    答:————
33.[问答题] 证明Wilson定理的逆定理:若n > 1,并且(n ? 1)! ? ?1 (mod n),则n是素数。
    答:————
34.[问答题] 证明:设ps表示全部由1组成的s位十进制数,若ps是素数,则s也是一个素数。
    答:————
35.[问答题] 证明:若2p ? 1是奇素数,则  (p!)2 ? (?1)p ? 0 (mod 2p ? 1)。
    答:————
36.[问答题] 设p是大于5的质数,证明:p4≡1(mod 240)。(提示:可由欧拉定理证明)
    答:————
37.[问答题] 若x,y∈R+ ,(1)证明:[xy]≥[x][y];  (2)试讨论{xy}与{x}{y}的大小关系。注:我们知道,[x ? y] ≥[x]+ [y],{x+y}≤{x}+{y}。此题把加法换成乘法又如何呢?
    答:————

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