巧用初中知识解@kenchung的方程式数学题 by jubi

cn · @jubi · Sep 17 '17 (edited)

$68.77

巧用初中知识解@kenchung的方程式数学题

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<p>偶尔去思考一下，避免自己迟钝下去。和我一起参加&nbsp; @kenchung &nbsp;的数学题，体会下思考的乐趣。希望大家多多支持 &nbsp;@kenchung &nbsp;的数学X编程比赛，下一期即将开始。</p>
<blockquote>&nbsp;传送门：<a href="https://steemit.com/contest/@kenchung/question-mathematics-programming-competition-6">[Question] Mathematics × Programming Competition #6 [問題] 數學 × 程式編寫比賽 (第六回)</a></blockquote>
<p><center><img src="https://steemitimages.com/DQmd5zSshfrWZDq88czhcXhSTqfB3T4At4S1MSv5zRASbR1/1%E5%89%AF%E6%9C%AC.jpg" width="400" height="200"/></center></p>
<p>&nbsp;题目：已知 <em>x</em> 為平方數，而 <em>p</em> 為質數，且符合公式 <em>x</em> = 1000000007<em>p</em> + 1。求 <em>p</em> 所有可能值之和。&nbsp;</p>
<p>乍一看被这个大数字吓到了，肯定会有人想用编程解决，毫无疑问这道题用编程解决是非常的快，那么从数学的角度来解答呢？其实一样很简单。</p>
<p><em>x</em> = 1000000007*<em>p</em> + 1 我们可以看作 x^2=1000000007*<em>p</em> + 1;</p>
<p>那么进行简单的变换下；</p>
<p>&nbsp;x^2-1=1000000007*<em>p 即</em><code><strong>(x+1)*(x-1)</strong></code><em>=</em>1000000007*<em>p</em></p>
<p>到这儿我们可以看出来 一个 1000000007*<em>p</em>是相隔2 的两个数相乘的结果。</p>
<p>1000000007*<em>p 的因数为：p、1、1000000007</em></p>
<p>那么显而易见，p 要么是1000000009 要么是1000000005 ，或者0 ，因为p是质数，那么就只能是1000000009了</p>
<p>根据条件进行简单的构造，问题就迎刃而解了。</p>
<p><code><strong>初中学习的x^2-1=(x+1)(x-1)还是挺好用的吗？有忘记吗？</strong></code></p>
<blockquote>除了数学比赛，还有 &nbsp;&nbsp;@armandocat 的 Coding challenge，传送门： <a href="https://steemit.com/contest/@armandocat/coding-challenge-2-win-sbd-if-you-solve-the-problem">Coding challenge #2 - Win SBD if you solve the problem!</a></blockquote>
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@tvb · Sep 17 '17

哪有什么编程方法，就是数学方法。编程的总得有个上限，他这个题，乍一看连个上限都没有。。。这题就是数学方法最好哈哈。我也发一个和你的方法略有一点不同哈哈

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@jubi · Sep 17 '17

还是比较简单的。:)

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@tvb · Sep 17 '17

我是把右边配方了，都一个意思哈哈哈。编程就确认一下那个1000什么7是质数能用上，其他我感觉也用不上。看看他的正确答案是怎么做的哈哈。

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@drunkevil · Sep 17 '17

最后一个等式对吗？怎么看着有点问题？

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@jubi · Sep 17 '17

x*x-1=(x+1)(x-1) 有什么问题吗

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@drunkevil · Sep 17 '17

文中好像左边没有减1。

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3 replies

@hannahwu · Sep 17 '17

太烧脑了 我不懂

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@justyy · Sep 17 '17

我去。这题我做错了， 我答案是0， 数学学不好。哎。

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@tvb · Sep 17 '17

太好了，我瞬间感觉我的春天来了。

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@kangnajiang · Sep 17 '17

原本还以为是一道编程题
结果居然可以靠初中知识解读，被数字吓到了

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@jubi · Sep 17 '17

是呢，表象。

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@catwomanteresa · Sep 17 '17

雖然數學不差，可是現在看到數學題都直接跳過，我是不是真的太懶惰了？

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@jubi · Sep 17 '17

就像我看到英语 大脑会告诉我赶紧打开百度翻译。哈哈

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@tvb · Sep 17 '17

咱俩一样呀，我发现咱俩有很多相似之处，问一下你胖吗？

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@kenchung · Sep 18 '17

我也是推介這個方法的~ 比較快捷
但是怎麼好像沒有看到你提交的答案? ...

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@tvb · Sep 18 '17

你这个题出简单 了，应该把1000000007改成合数。这样首先需要计算出1000000007的质因数，再计算所有的可能的约数，再去循环来做各个约数可能存在约数=1000000007/约数XP+2或-2。这样就是程序题了。现在基本就数学题。

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@kenchung · Sep 19 '17

你這提議不錯的，當時想不到啦 haha

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1 reply

@armandocat · Sep 19 '17

Unfortunately I don't speak Chinese. I've posted my solution here for who's interested 😼
https://steemit.com/contest/@armandocat/my-solution-to-mathematics-programming-competition-6

👍 armandocat

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