(2001 年，北京初中数学竞赛题) 1和0交替排列，组成下面形式的一串数
<br /="/"/><p align="left"><font face="MS Song" lang="ZH-CN">101, 10101, 1010101, 101010101, ...</font></p><p>问在这串数中有多少个质数？并请证明你的结论<div></div><span style="display:none;">www.ddhw.com</span><br /="/"/><br /="/"/> <div style="MARGIN-TOP:20px;MARGIN-LEFT:0;MARGIN-BOTTOM:0;float:left"></div></p>回复：(2001 年，北京初中数学竞赛题) 1和0交替排列，组成下面形式的一串数
<table cellpadding="8" height="100%" width="100%"><tr><td valign="top"><br /="/"/>Only 1. We know 101 is prime. For any other (call it n), n * 11 = 11....11 (2k 1's for some k > 2) = 11...11 * 100...001.(First factor contains k 1's, second k-1 0's.) Now one of them is divisible by 11, and the other devides n.<span style="display:none;">www.ddhw.com</span><br /="/"/><br /="/"/> <div style="MARGIN-TOP:20px;MARGIN-LEFT:0;MARGIN-BOTTOM:0;float:left"></div></td></tr></table>Great! [:B]
<br /="/"/> Great! <img /="/" border="0" src="/img/6.gif"></img><br /="/"/><br /="/"/><br /="/"/><br /="/"/><br /="/"/><div style="MARGIN-TOP:20px;MARGIN-LEFT:0;MARGIN-BOTTOM:0;float:left"></div>Thanks for the question
<table cellpadding="8" height="100%" width="100%"><tr><td valign="top"><br /="/"/><div>Thanks for the question. It gave me the idea to solve this problem in WXC:<span style="display:none;">www.ddhw.com</span></div><div> </div><div>The repeat of a positive integer is obtained by writing it twice in a row (so, for example, the repeat of 254 is 254254). Is there a positive integer whose repeat is a perfect square?</div><span style="display:none;">www.ddhw.com</span><br /="/"/><br /="/"/> <div style="MARGIN-TOP:20px;MARGIN-LEFT:0;MARGIN-BOTTOM:0;float:left"></div></td></tr></table>Why?
<table cellpadding="8" height="100%" width="100%"><tr><td valign="top"><br /="/"/><div>Could you explain more? We need to show a factor in n. I do not see your reason for it.</div><span style="display:none;">www.ddhw.com</span><br /="/"/><br /="/"/> <div style="MARGIN-TOP:20px;MARGIN-LEFT:0;MARGIN-BOTTOM:0;float:left"></div></td></tr></table>I got it
<br /="/"/> I got it<br /="/"/><br /="/"/><br /="/"/><br /="/"/><br /="/"/><div style="MARGIN-TOP:20px;MARGIN-LEFT:0;MARGIN-BOTTOM:0;float:left"></div>Your question is interesting, why don't you post
<table cellpadding="8" height="100%" width="100%"><tr><td valign="top"><br /="/"/><div>it here as 加 新 贴 ？ <input /="/" src="http://www.topchinesenews.com/img/1.gif" style="CURSOR: default" title=" 顶顶华闻http://www.topChineseNews.com " type="image"/></div><span style="display:none;">www.ddhw.com</span><br /="/"/><br /="/"/> <div style="MARGIN-TOP:20px;MARGIN-LEFT:0;MARGIN-BOTTOM:0;float:left"></div></td></tr></table>I will
<table cellpadding="8" height="100%" width="100%"><tr><td valign="top"><br /="/"/><div>All right. I did not because I thought people here like only the quick-wit type of problems.</div><span style="display:none;">www.ddhw.com</span><br /="/"/><br /="/"/> <div style="MARGIN-TOP:20px;MARGIN-LEFT:0;MARGIN-BOTTOM:0;float:left"></div></td></tr></table>回复：(2001 年，北京初中数学竞赛题) 1和0交替排列，组成下面形式的一串数
<table cellpadding="8" height="100%" width="100%"><tr><td valign="top"><br /="/"/><div>101一个</div><span style="display:none;">www.ddhw.com</span><br /="/"/><br /="/"/> <div style="MARGIN-TOP:20px;MARGIN-LEFT:0;MARGIN-BOTTOM:0;float:left"></div></td></tr></table>
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