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问题 解答题
设p，q均为自然数，且
p
q
=1-
1
2
+
1
3
-
1
4
+
1
5
-…-
1
18
+
1
19
，求证：29|p．
答案

证明：注意到29是质数．令a=10×11××19．

p
q
=1-
1
2
+
1
3
-
1
4
+
1
5
-…-
1
18
+
1
19
，

=（1+

1
2
+
1
3
+
1
4
+…+
1
19
）-2（
1
2
+
1
4
+…+
1
18
），

=（

1
2
+
1
3
+…+
1
19
）-（1+
1
2
+…+
1
9
），

=

1
10
+
1
11
+…+
1
19
，

=（

1
10
+
1
19
）+（
1
11
+
1
18
）+…+（
1
14
+
1
15
），

=29（

1
19×10
+
1
11×18
+…+
1
14×15
），

∴ap=29q•b，

其中b=a（

1
10×19
+
1
11×18
+…+
1
14×15
）是整数，

∵29|a•p，29是质数，29|a．

∴29|p．

单项选择题

常见的较小的第五牙尖位于（）

A.颊面与远中面交界处

B.颊面与近中面交界处

C.舌面与远中面交界处

D.颊面与近中面交界处

E.中央窝
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单项选择题

Questions 53 to 57 are based on the following passage:The Internet can make the news more democratic, giving the public a chance to ask questions and seek out facts behind stories and candidates, according to the head of the largest US on-line service.’But the greatest potential for public participation is still in the future,’ Steven Case, chairman of America On-line, told a recent meeting on Journalism and the Internet sponsored by The Freedom Forum, though some other speakers say the new technology of computers is changing the face of journalism, giving reporters access to more information and their readers a chance to ask questions and turn to different sources.’You don’t have to buy a newspaper and be confined to the four comers of that paper anymore.’ Sam Meddis, on-line technology editor at USA Today, observed about the variety of information available to computer users.But the speakers noted the easy access to the internet also means anyone can post information for others to see.’Anyone can say anything they want, whether it’s right or wrong.’ said Case. Readers have to determine for themselves who to trust. ’In a world of almost infinite voices, respected journalists and respected brand names will probably become more important, not less,’ Case said.’The internet today is about where radio was 80 years ago, or television 50 years ago or cable 25 years ago, ’he said. But it is growing rapidly because it provides people fast access to news and a chance to comment on it.

Which of the following statements is true

A．Only respected journalists can post information on the internet for others to see.

B．Respected journalists will probably become more important than before.

C．When people read newspapers, they have to stay in the comers of the street.

D．The greatest potential of public participation of the internet is in the near future.
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