西南大学22年9月0346 初等数论在线作业题目及答案
0346 初等数论1.[单选题] 6的欧拉函数值是（）。
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A.0
B.1
C.3
D.2
2.[单选题] 下面的（）是模10的一个简化剩余系。
A.11，13，17，19
B.11，12，18，19
C.11，15，18，20
D.11，12，13，14.
3.[单选题] 下列数中是3的倍数的数是( ).
A.5550
B.5551
C.5552
D.5554
4.[单选题] 下面的（）和7关于模10同余。
A.13
B.10
C.-10
D.-13
5.[单选题] [-1.6]=( ).
A.-1
B.-2
C.2
D.1
6.[单选题] 大于20小于40的质数有（ ）个。
A.A.7
B.6
C.5
D.4
7.[单选题] 15的最小质因数是（ ）。
A.3
B.1
C.5
D.15
8.[单选题] 下面的数组是勾股数的是（）。
A.（3，4，5）
B.（1，2，3）
C.（4，5，6）
D.（2，3，4）
9.[单选题] 不定方程32x+25y=1( )。
A.有正整数解
B.有整数解
C.无整数解
D.有负整数解
10.[单选题] 在30！的标准分解式中，质因数5的指数是（）。
A.5
B.7
C.8
D.6
11.[单选题] 如果( )，则不定方程ax+by=c有整数解。
A.(a,b)|c
B.(a,b)|b
C.(a,b)|a
D.c|(a,b)
12.[单选题] 下面的()是不定方程5x-2y=1的一个解。
A.x=1,y=2
B.x=1,y=1
C.x=2,y=1
D.x=2,y=2
13.[单选题] 下面的（）是不定方程3x-y=10的一个解。
A.x=2,y=4
B.x=1,y=1
C.x=4,y=2
D.x=0,y=0
14.[单选题] ( )是不定方程<img class="kfformula" src="data:image/png;base64,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" data-latex="x-2y=10"/>的一个特解。
A.x=1,y=1
B.x=0,y=1
C.x=1,y=0
D.x=2,y=2
15.[单选题] 下面的（）是模5的一个简化剩余系。
A.2，3，4，5
B.0，1，2，3
C.1，2，3，4
D.3，4，5，6
16.[单选题] 如果b|a，a|c，则( )。
A.c|b
B.b=c
C.b=-c
D.b|c
17.[单选题] 下面的（）不是模5的一个完全剩余系。
A.3，7，12，15，20
B.5，7，9，11，13
C.1，2，3，4，5
D.2，4，6，8，10
18.[单选题] 关于模7，下面的（）和2同余。
A.17
B.15
C.14
D.16
19.[单选题] 把8表成两个质数的和，其表示式为（）。
A.D.1+7
B.3+5
C.2+6
D.4+4
20.[单选题] 小于200的正整数中有（）个是7的倍数。
A.E.27
B.28
C.30
D.29
21.[单选题] 10与12的最小公倍数是（）。
A.60
B.10
C.12
D.120
22.[单选题] 大于4且小于15的素数有（ ）个。
A.2
B.10
C.5
D.4
23.[单选题] <img class="kfformula" src="data:image/png;base64,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" data-latex="x{}^{2}\equiv 1（mod5）"/>是（）次同余式。
A.2
B.1
C.4
D.3
24.[单选题] 下列数是合数的是（）。
A.3
B.4
C.2
D.5
25.[单选题] 若<img class="kfformula" src="data:image/png;base64,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" data-latex="a\equiv b(mod\, m)"/>,则下列说法正确的是（ ）。
A.B.a是m的倍数
B.a+b是m的倍数
C.a-b是m的倍数
D.b是m的倍数
26.[单选题] 整数637693能被( )整除。
A.3
B.5
C.7
D.9
27.[单选题] 6的所有正因数的和是（）。
A.3
B.6
C.12
D.2
28.[单选题] 下面的（）是5的倍数。
A.20
B.12
C.16
D.24
29.[单选题] 4除17的余数是（ ）。
A.0
B.3
C.2
D.1
30.[单选题] 下面的（）能被9整除。
A.66
B.33
C.69
D.36
31.[判断题] 由于5整除15，所以5是15的因数。
A.正确
B.错误
32.[判断题] 如果a|bc，则a|b，或者a|c。
A.正确
B.错误
33.[判断题] 如果(a,b)=1，（a,c）=1，那么（a,bc）=1。
A.正确
B.错误
34.[判断题] 整数a与b的公因数的因数一定是a与b的最大公因数的因数。
A.正确
B.错误
35.[判断题] 大于3的质数除以3的余数一定是1。
A.正确
B.错误
36.[判断题] 二次同余式<img class="kfformula" src="data:image/png;base64,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" data-latex="{x}^{2}\equiv -1(mod\, 5)"/>无解。
A.正确
B.错误
37.[判断题] 模m的一个完全剩余系也是模2m的一个完全剩余系。
A.正确
B.错误
38.[判断题] 6和8的最大公因数与-6和-8的最大公因数是相同的。
A.正确
B.错误
39.[判断题] 一个质数不可能是11的倍数。
A.正确
B.错误
40.[判断题] 如果a|b，b|a，那么a = b。
A.正确
B.错误
41.[判断题] 把<img class="kfformula" src="data:image/png;base64,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" data-latex="\frac {1} {6}"/>化为小数是一个无限小数。
A.正确
B.错误
42.[判断题] 设p为质数，则p的欧拉函数值为p-1。
A.正确
B.错误
43.[判断题] 模m的一个简化剩余系中的每个数都与m是互质的。
A.正确
B.错误
44.[判断题] 如果两个整数互质，那么它们没有公因数。
A.正确
B.错误
45.[判断题] 模m的一个完全剩余系中一定有两个数对模m同余。
A.正确
B.错误
46.[判断题] （-364，258）=（364，258）。
A.正确
B.错误
47.[判断题] m个连续整数一定构成模m的一个完全剩余系。
A.正确
B.错误
48.[判断题] 不定方程2x+4y=6与x+2y=3的整数解相同。
A.正确
B.错误
49.[判断题] 模m的一个简化剩余系中的每个数都与m是互质的。
A.正确 重庆大学答案
B.错误
50.[判断题] 一个二次同余式最多有两个解。
A.正确
B.错误
51.[判断题] 整数a的个位数是9，则a能被9整除。
A.正确
B.错误
52.[判断题] 39993可以被3整除，也可以被9整除。
A.正确
B.错误
53.[判断题] 偶数个奇数的和一定是偶数。
A.正确
B.错误
54.[判断题] 不定方程8x-2y=16无整数解。
A.正确
B.错误
55.[判断题] 如果<img class="kfformula" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALMAAAAsCAYAAAAuJIllAAAIz0lEQVR4Xu2bd6xtRRXGf6BgAxUBkZIoarBFREUioYWgmBBUYu8NFRWVTijSpFhAmhUrKhI0amzRoDGxEVtUVBAwGhVEKREjHYJAfmQtMhnPOe+ck7v3e+49+5+Xd++e2TNrfWutb30zdy3a0ywwEAusNZB9tG00C9DA3EAwGAs0MA/GlW0jDcwNA4OxQAPzYFzZNtLA3DAwGAs0MA/GlW0jDcwNA4OxQAPzYFzZNtLAvBwGHgjcCty53PBBjxJTDwBuAe7qc6cNzItZW3vtBdwX+HLfzlpsqav17Z2BJwCfAu7oayUNzItZehfgacAH+3TSYktcI94WVy+LlZzXV9CPGczPAo4AngLcBjwX+NUMKGwOHAUcC1y1RkBm/kU8FXgP8HjgkcDzgW/MP3ypNx8EnAB8BvjdUjMsOGjMYNZUct8zgEcBrwCunWK/+wCHApcBX13QxmvK6/r6GOAFwEuAS3tY2HbAq8N2cuhOn7GD2Sx1LvBz4DDg9inW3hI4ETgI+GenHulu8ocAn4zp3wj8p7tP3Tuz2fm0+O4vuv7e2MG8A/Ad4O3A52YY+5VAArrXDn0FASDF+FJUluP64rHA3sCmkQw6td3YwbxPlN5ZfFmZyezyFeB7Kwiuvqd6HvD1nvhyubetgSOBtwD/7nLTYwZzgvQxq+DLmwEfBg7viWd24e/ky/YFL+qrIYuNbAx8PJJGp43g6gCzzZac7e+h114JXAdsEiWw1iWfDnwzStUyjv4EsD9wczVYkH4hmrofABuFqvFE4FTginjfzGJZfvOUBlHN2axjM/lY4CPAJaFHW15VPp4TuvS3Q014OfAXYKuwwelhg2n7e1w0UtpMXv9k4GOx9nqMPnXNrwUuBtznL6Pc+27Nl7X7fnHIcb/Yuw2v468BNggV5GTgr4Aa8o4x9x7A92Nv0/TkbLKlOJ1Wtr7BrCGUt2y2lMH8/gHAB4DPA/sCNyyD2CXGPBP4LvCH+G7KclKP3QD/tSzKqw2GaU2THbtzeUDgPgSHASrYLop1vSb2fBYgYNSp7e4zoJTJpDL1Y6C8CVBGfGfM6zu7R4C9IQInx2nPlwIvLt7PCuR+lOe0/39jgO+/A/hZNIRfBH4MXA+8N3yRYFwvvmUjd35w7mcDn12FrLluzKV9TR6dPX2C2RMhNccPxaayGRAsPwkjqxh02iQUltS5ZhvLrqDOJ5tCAaOTbf52iqCr5SXtp8Lh+L9F1/6MyGo/LOZMvmqVMHhvit9tGLYw4/nzcn7nFqxvjaxsts/H0q0K89MAdYLTQx0p0duAHxXvG0yCrtaXrUZ+V+BaJayAglXbXB3jE4y+p8wmIGvfvWoVQDWAzNwGU2dPX2Au+amGLeWt1dGY3D+yqJRCsP6jsLDVQyCmg2aB+cHAwTGXAPO0y7Jrw1OWXYFwSFCPUqKSljjmWwHKMpC3jfJ9ZmTt8ncZBFaxrBhSGhUZqYjqTAbMLL68TVQeA8CM7lqkDio8+aSkJ/VQmSibuBxjEJXBUwNWMPsc3xmSo8x3OX/ObSn+GnB2VeY0kBvcs0ch3zVlef/NBH3ZrCRF8DjWsjsLzKXtLLlm6Dr7zWo0M3DqMVKR9wddmKS0ZBDIx82WAszDEBUXwS3lqcHo/6dRpfSDoLRJtMrkI1/XDvqvlPQySNx3PWbQYDYz2VTVTptHyDcQzBQPWzLqJjWA2VTqHHlsPpNAZOUwW9U0oF6OasfrJ6gFswLHOW20zHCeLuaThzk2rZNOJpMKeQhi/+EjVTAAa/AnGG0+S75crt8mz57FRrzuW6YFafruX3PYxu/eOKUvWNKt/zusD5qRJV2j1LKQXbe3z+R/fQr5gkeQJy+uQSRfzJIqcARqZsBJxl8/uKoBV7+XjaY0owycWWDIMQJMTu5103zKpvmFoQAlGD1xq2nTPDQu/WBPU/PaaUGaCcF9zWrssjLZWP7fN4CzymxpaJsPO2szyJ9WLFwnT6TDdUKdES3VUiEB6QGDj5ntpFhbya3LmTOTyrXr7DftYKYGgxXIG3lSnPzdRyfwTIGbNMK5vU+SHFo5UZktZUiBL3+3TzGR/Dn4tPOqWOSTfjC4S/ksg1Qf1hSlrCp/jHkF7IWVyXMOA/mCLv3aR2ZOg6pNCiLLkk+e25uFvPhiU+hlHrli1/cGzLZeMHI9Wd4FiQYXHK4jG6gEj0rLtFt1WYrrrn5WoykQLenu3TWoWhgMasPZzOn8mqe65nfF2nM9mTC0a0mHHhEKixKf41QvzObvK+S55MtSqTq4k5vbC5RBmgD1tqHBIz1zL8qLabey2mlrG+VOk1QfYHZTduZKcpZuneXm7bgFgQbXiJZdZS0PHcrOvYtDkwSuZVU+rrMt50+Kf8vbczrb22YCblqZTLWi5qvJl9Wya7rgGA9TBNnDQ9s2K6uC6BcPVrSLoLfR82e7AkcHT1Y2LB/7ESW510ViEHBShO0DRILO+S4PxSXHzupbMkizGa7HeKLnNU8D0jWWcmS+a+LwwEl/d3qG0BeY0xGWs1/HpR1lIBuOvB+8dgB52jXMla5Qjw4D6xBBLDiUyMw29eMhioqLzVb9+3Uie5pND6ykK4/KDRj1bGlU+WwR41RUnMMj3zKrGWCCyW+rw3vqp720W1a3cj7fl0r4nhlQqdBvPzSy6u9Dx7ZXKPfgOnzPq60GU5lInM/TTZNQqXD4XddmcDivp5nurz4jSH5vpS0VlpX25T3z9QXmThbf46Rmco+cpUBWlvbMZwED3FNRebuA7/RpYJ7fvJZxr1GeUvDN+UeP883k6R78dH6y28A8P8hsWOXO5/R862z+Fa5Zb/pnZv5Z2ruLo/FOV9jAvJh5vURkV252zrsLi80wjrcNfIFs4Jd3SjrdfQPz4uZVU1bG+vSUZnHxGYc1wkZe9eO3ffcXDczDAtKod9PAPGr3D2vzDczD8ueod9PAPGr3D2vzDczD8ueod9PAPGr3D2vzDczD8ueod9PAPGr3D2vzDczD8ueod3M3sx0NS9wkpfgAAAAASUVORK5CYII=" data-latex="a\equiv b(modm)"/>,那么m能整除a-b。
A.正确
B.错误
56.[判断题] 两个整数相除（除数不为零），其商一定是整数。
A.正确
B.错误
57.[判断题] 两个奇质数的和一定是合数。
A.正确
B.错误
58.[判断题] 贾宪数<img class="kfformula" src="data:image/png;base64,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" data-latex="\frac {n!} {k!(n-k)!}"/>是整数（0<k<n）。
A.正确
B.错误
59.[判断题] 2是模5的一个原根。
A.正确
B.错误
60.[判断题] 一个质数只有两个正因数。
A.正确
B.错误
61.[判断题] 一个整数能被4整除，也能被6整除，则它一定能被24整除。
A.正确
B.错误
62.[判断题] 不定方程2x+8y=7无整数解。
A.正确
B.错误
63.[判断题] 若<img class="kfformula" src="data:image/png;base64,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" data-latex="a\equiv b(modm)"/>,则a-b是m的倍数。
A.正确
B.错误
64.[判断题] 不定方程3x-6y=9有整数解。
A.正确
B.错误
65.[主观填空题] 勒让得符号<img class="kfformula" src="data:image/png;base64,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" data-latex="\left ( {\frac {4} {7}} \right )=\, "/><span style="text-decoration: underline;"> </span><span style="text-decoration: none;">。</span>
A.
66.[主观填空题] 18的质因数有 。
A.
67.[主观填空题] 16除-81的商是 ，余数是 。
A.
68.[主观填空题] 6与10的最大公因数是 。
A.
69.[主观填空题] 10！的末尾有 个零。
A.
70.[主观填空题] 模3的绝对最小完全剩余系是 。
A.
71.[主观填空题] （1516，600）= 。
A.
72.[主观填空题] 20的标准分解式为 。
A.
73.[问答题] 解同余式<img class="kfformula" src="data:image/png;base64,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" data-latex="3x\equiv 2(mod5)"/>。
A.
74.[问答题] 求不定方程3x+10y=7的一切整数解。
A.
75.[问答题] 解同余式<img class="kfformula" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALYAAAArCAYAAADVCHKZAAAJq0lEQVR4Xu2bd6x9RRHHP6CCYhRQECUkKiJFgVhRwYAFC4pIUURsGCuKFRSQgB3sQGwgGBAFLGgUKZaoUfQfjSV2QMEuYEMQUWPLh8wkm+Xc33v3vnPOu+9mNyEk757dnZ35zsx3Zve3Hm00DSygBtZbwDO1IzUN0IDdQLCQGmjAXkiztkM1YDcMLKQGGrAX0qztUA3YDQMLqYEG7IU0aztUA3bDwEJqoAF7HLOuD9wa+Ps4283NLqt27gbs4TFwW+DFwGeBnwy/3VztIL6eBPwb+DTwv7Gka8AeVtO3BF4CfAf46rBbze3qq6KDBuxh8fBo4AHA2yJqDbtbv6vfFzgB2B64K/BE4PwZt7gz8DrgjcBvZ1xjqmljAvupwK7AByIl/xfwwE8D/ga8fyrJV+fjDYF9gXsDtwnQfhL4MPDXSqQ7AW8JY165OuKueFfx8Vpgf+BA4KfViupj76AblwJbAp8BLuqgHa6xXTj5f1Ys2RILjAlsAfyRSp5fhuI+Cvxz6MOucH2NeChwCfDtWEvHNBrfHngBcHWxh4a8D/B6YHBDrvBsk6ZvDJwePz63ct7bheMKdoOV9pN2HBl8+kfVoncB3gkcAwzu6GMD+1rgGsCCShD8HPjXQEbpe9lHAkbhc6uFdwZ0TKOURtPARvN3hSN/o29BRlxPGvJx4FPhoFn8CWAdVmfPMyvW4yJ7vQj4WCXnLSKIGdnPHvoMYwP7F8BaNPQGwKvDaGaZcgjiE4GdgIMBfzflHh+F4++GNuKA6+8T1KLm17uH4z4LKCOzOnhNnP0HHXI9Kqjc4cA/BpR71GerUpG1CuxNA9SbAIcAP6uMcizwBuCh4bgaUE76sjXcu05+rbPasvt+nNkoLf1SJ7Yxr58CoGYAC1LnDerw8xyxle1BwGOBPwLbAG+Oiw6d5CrAyv1k4IpCuSreaPnKKRRefvpnYD/ga8Ufjcqu+cAOYCcAng88Ifi3fFtOabru6t2ayl8IbBTnel8U1BamzvNsjwHOC4pjV8LiW266bXDZkwBl7RrKtAvwZOC7wObAHaNA7wKU30upMgJbBH4LeE4Hv1aWc4DPRWE8jZqVQz5uQZqOMs38ZX87NrBvDMP9Kbj1g4NvecgaAHsA9wPeHb/ZKhLcvwbeFIYT1B+KKLDsQ/f8oUXUe+NczwR+DxjB7fRIUbqGoPPsH4yCaotog50C/DAmuNZRwKnBZdWD+hN0clRbb13rW7847w7xfyOqdrb4e3xHketvTwkneGnIkfRKBzXCep4sgJX7C4A8+jfAjpHB7h/OeeE6GgFZjOqUg1LSsYEtME1jGshxtzCc0bC8wLBIU3EWYNfFt6av9wAHRDFjh8K/qfxBlbSEIwhSb9WMQnYQvDoXcHZPuookdS7HFBzyceeYCYyWpQ6S354GvAK4IeQw8rqutM6/py792UwgCAWZQDby58hC0GCgQ+UwgOiY6rvMUjqWQaPm1zqBxbLFoXJcEIHHvXUo5ZNnl3LlXukwX+koLnuNN2MCW4N7tep/OdzfqlrDPi86Jv4mRzUSWo07LN7sCdsHz5TcqyJmXMw2n5HU6GxxKfjSeJOA7ZwjIlKbmgXJl0IPpW4E7aui2PpmIZ/BwTkCqqY6gtCeunVA6i6nWtAKxi8HAO1GSXvOish7WOE8k/i1a2Xb9kygnONv2SF6eThurdaldDOjGW4+bUxgTxI6I5O3dF+c8NFmYbA/zFCw9KasaiEjlJH3HgGU5LvTGE8HNnLXUTHXcG2LN8+dw46Ekb2eYzFnJJbWZHemFDkphMDProS9di+YjO5lFF9X/zqBbQ1TU6HMJj8unKeUYRrdrMhu8wDs3YCvRzEln+waplYfEb19Hbw151k8+p1vNGYZXcVjvY56M3OYxo+uirjMLl7iLNWvde6zq66DeyWPtvAzvZe9fiO5tEVKYE84R+pIjtvVjakBmXIeVBS9dXS3N1/ya39Pez2943wJbDPPM4C/VIpLYLvurNfzy7LpGMB2D/naw4DjovgrhUtF+ZsFYteQRwvWvVaZTyub53l4dC1s8SX3LeUWDBrXwmvSyKLTIq8GQUZXqUjp7BlJLb5rfp3cV35b75stOrskdl6kNtnCtNgU9GW3ZFL/2rMkV5eX14FoKWDn79p50LpoDGDLrb1KFcCmSNNUOSal4/wmvVyOWBrAtpO9YgvMMa+sjdICW0crQX3PKBy9mFBO35PU0a48d7bNpBX1dzqyxWi2D+uoLODNBhaudo7spiQYuyLp3ePG1BaetYCFXYLMLlMZ4bPuMRjZv/Z2WC7tWx4L+XSuyzvktmawFeg+XWc3E1mT6HxltllWFJ7mozGArTymW191ySfLkUp8REQtv5EjenhvplSoBvAaW8CkAZxngaTSy0p+mrPP8u0OEamNVHXVb8T0vbWtSyOuHNSCuH4clfumQ9dAzEBwr45IKuDtBOnQAsPOkI7h7Z+O9Ikosi0Ic2S3wicB6ixvTjNg+F0Z/X3/YqfGeTqo9Y2dqLcWAcT+thQm25u5l47mFby/WxDXQ7pks8Dfa5oyiz0mzhkL2HqyFbwXEdmnzZRut8MuQQJUUPhC7B2A/U4LG6OhlzEZse2ieHljpCo7CR50iAsa1xXURjsNV4NaMFqI+TTTlG63QdmlV5MiU3Y96qic/NrMVl89O8eLG/VgS1Swpg7KYjbbg/4LFrOkFEQdG2XLYQFqm0/A23+XHsn7HxK9aQOJDvurCqjSF9u2OrHtSF9qOlfw6zhm6Nou7rucTNYLwMcCtsKqDKOT75O9Qds6+qzeRKm4HH7nrZwXNrbRLgtOKMCN5l4KmBK9lRvrRaAtOuXUyJOGUS4zSj74+V5H2835twpH1wGM7GX0shNyRlAdC+ZybBXzLCpdQ5lKOmQUNppLPdxb5zfTGSi6agGdQbrhGw+fCRiA3NunA1IJ5+rEgrfWtUA2g8i5BbMZxs6K7USBXg8DjkHMNmVXNO8F0LnImMDuVfA1sJhpWWcsL1fWgNiDiShVMuPZ4x6UhniCBuzB7HgTJZKaXDxyHTDciWZf2QwmFfLtttlj8NGAPayK5eU+jrLDkU8Dht1xPlf3RlIaap3VRYl6l7oBu3eV3mzB8jFXV0E1vASru4N1kdHaZkD5L4wGlaoBe1D13rS4Ot4TsEPx+eG3m6sdpGN2XCwYR/lHvK14nCv7N2H61kCL2H1rtK03FxpowJ4LMzQh+tZAA3bfGm3rzYUGGrDnwgxNiL410IDdt0bbenOhgQbsuTBDE6JvDTRg963Rtt5caKABey7M0IToWwP/B7YsHkrMBk72AAAAAElFTkSuQmCC" data-latex="5x\equiv 2(mod6)"/>.
A.
76.[问答题]
解同余式: 28<em>x<img class="kfformula" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEcAAAArCAYAAAAqhpU+AAAAwElEQVRoQ+3WuxGCQBgA4aUFM+twxrrsxzIM7MzYCnCGBc4LlpjjsffxDwsdqwWW2qwXKM4PHcUpjhseyUlOclyB5LhuzZzkJMcVSI7r1sxJTnJcgeS4bs2cieTcgBdwdXvJE3gAH7l+07LkTCRn0879++TkJMcZHC3nDryBi3vcBrLsdvyy0XKOf4MTr1iciQZyP4EnSh966T6riT6roTu/92bJSY4zlJzkJMcVSI7r1sxJTnJcgeS4bs2c5Dg5X3w7CSzmONSNAAAAAElFTkSuQmCC" data-latex="\equiv "/></em>21(mod 35)。
A.
77.[问答题] 证明：若（a,8）=2，（b,12）=2，则（a+b,4）=4。
A.
78.[问答题] 证明：若 = ，则|x-y| < 1。
A.
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