奇特的日本考试题，质因数分解83333

[@佐藤広-c4p]

I watched the original video. The question maker is said to be a first-year high school student. The instructor is young and very smart, but he seems to be surprised at this flexible idea of factorization. 3333 to bring it in the form of "(… 0000) ^ 2- (1) ^ 2" so that the factorization formula of a^2-b^2=(a+b)(a-b) can be used. It means that the part is tripled to 9999, but unfortunately, there are no convincing comments about the basis of the idea or the theory.

[@wuchinren]

But he SHOWED AND ONLY SHOWED that "833 and 83333 and 8333333 and 833333333 and 8333....333(8 followed even 3s in back) are all composite". Is he wrong?

[@佐藤広-c4p]

@@wuchinren 様 I'm an ordinary person, so I can only understand it by multiplying it by 3 so that can be used the factorization formula. However, a more knowledgeable person who is close to a super enthusiast(otaku) or an expert may be able to explain more theoretically.

[@wuchinren]

@@佐藤広-c4p Briefly (in short), 51 and 501 and 5001 and 50001 and 500001......must be divisible by 3, right?

[@佐藤広-c4p]

@@wuchinren 様 The number of this problem is multiplied by 3 so that the factorization formula of a^2-b^2=(a+b)(a-b) can be used conveniently, and the square is difficult to understand, so b=1. Then, if you multiply it by 3 and add 1, it's good if the number is in the form of x^2. This problem is (83333)*3+1=249999+1=250000=(500)^2, (83333)*3=249999=250000-1=(500)^2-(1)^2=(500-1)(500+1)=499*501=(499*167)*3. Other numbers are whether they look like this. Please check for yourself.

[@wuchinren]

@@佐藤広-c4p Satoh Hiroshi sama: Did you explain the problem to me? Then I may misunderstand your words before. In fact, I know how to solve the problem perfectly. So we were just trying to explain the problem to each other.

[@pptrar]

真的 遇到這題，我一定先跳過和放棄，太花時間了，不如先看看該題分數比重。

[@ip-Animal]

這思路很棒,還有這種方法阿

[@FrankACai]

如果直接分解，會變成291^2-1348。那就等於還是要暴力分解

[@劉達宗]

有趣的技巧，不過在質因數分解這個目前是無泛用解的題目上這種小技巧總覺得有種誤入窄路的感覺。

[@wuchinren]

但如果只是要知道某類特殊形式的數是不是質數，而不要求把它完全分解，那顯然是有用的。 例如999.....9991(1前面接奇數個9)必然不是質數。

[@ugxjaaadj]

好神奇，考试遇这种题我都是放弃的

[@jerrywang8450]

这类题有点初见杀，看了一次记住了就会比没看过占太多优势

[@hakacn]

所以要想取得优势，就要多看这类题

[@hubenbu]

他大爺的，這麼有趣！質因數分解原型態就是相乘。

[@星E君]

你在教我们手动破解RSA算法？

[@ycyu8979]

有意思，3连数变9连数，9连数增减1变因式分解。只要做过一次，再遇到就好办了。

[@wushanvlog]

确实是的！

[@jadey5621]

這種日本魔術解題的題目毫無意義。我們在高中都浪費太多時間在這種爛題上。結果是你必須做過千萬題目，冀望高考時能出現一兩題。

[@sjdicky02]

學校的數學是在篩選天才

[@weirenwang9100]

判断质数那个是应试的，并不严谨

[@qqqquito]

方法奇妙！

[@残酷的真实世界]

这个叫做配1法，1是一个很特殊的数字。

[@123xiaotai]

想问下看这些视频的人都多大啦 都是学生吗

[@joe20011021]

那是怎麼知道不是3個質數相乘的?

[@selflu4763]

如果还可以分解成3个质数， 就是说，m x n == a x b x c , mnabc 都是质数， 这个等式是不可能成立的。

[@SaderGP]

影片 3:42 就是在驗證是否還能繼續質因數分解 最後確定 167 和 499 都是質數 也就是83333的質因數分解 分解完畢

[@defang6361]

分解成两个数之后如果其中一个不是质数就继续分解就可以了

[@EurekaZhuJinxuan]

@@LoveTaiwan678 最開始的分解是為了分解成兩個奇數的乘法，而不是為了分解成兩個素數的乘法。

[@LoveTaiwan678]

@@EurekaZhuJinxuan 謝謝

[@ironkyoater]

幹，這題解決了以前我們數學老師教的，但是又沒教完的題目。

[@Celank]

I've known this idea, but I learned this in perfectly same problem... I don't know another one by using this idea.

[@晴海無雲]

這是特殊解 只適合少數題目

[@fdr2275]

This kind of math is meaningless because the problem can be solved easily with a simple computer program. The following would be a better example for illustrating the power of algebra in solving problems which cannot be solved by computers using brute force. Given: a, b, c are positive integers; a/b = b/c; a + b + c = 8,191,000,273,000,003 Find: a, b, c

[@walty80]

Most problems can be solved by simple computer programs now, but that does not mean they are all meaningless. And what's the point to learn multiplication when it can be done by a $5 calculator? It's about logical thinking and insight exploration.

[@fdr2275]

@@walty80 Learning multiplication is a different story. In the old days, we were taught only the multiplication algorithm. Today, at least in the US, elementary students were taught not only the algorithm but also the theory behind the algorithm so that when they grow up and go to college, they know how to build new mathematical models. Yes, you can always argue this kind of problem can train students to think logically but what I am saying is university entrance exams should make up problems that are practical and at the same time can test students' ability of logical thinking and insightful exploration and there are plenty of problems of this kind. Problems like this one give people the impression that mathematics is a piece of joke that is used only for entertainment.

[@釋寂參]

大大好玩

[@seanming75]

這題本來就是故意要你放棄的，這場考試設計應該不可能全部寫得完，考你怎麼分配輕重緩急。

[@覓糖-g5b]

這種0與100問題 没意義 也可以解讀成這場考試是設計考你會不會向困難低頭而放棄

[@lutmingtsoi8460]

可怕是，有人把題目全都寫下，並考得滿分。

[@YanxinHe9186]

@@lutmingtsoi8460 所以我一直觉得，一般人学习奥数就是背题型而已，看到新的题型还是不会。真正聪明的人看见新的题就有神奇的思路根本不用学，笨的人学再多依旧想不出新思路，所以学奥数的意义是什么🤔

[@ymj5161]

还是一个一个质数试吧，没有捷径可走

[@鄭雷丘-l4g]

但先開根號會更快 這是質數性質

[@鄭雷丘-l4g]

從奇數3開始

[@isaac893]

1,167,499,83 333

[@marshalls36]

好

[@吳鎧全]

但是，誰會一開始想到呢? 暴力破解還是有希望的，

[@nnknill7724]

这不就是费马9岁玩的

[@Sailor999999999999]

感謝神，我有計算機。

[@一-m9c]

用計算機算給我看阿

[@mikeli9532]

高啊！

[@周鑫说]

167、499

[@abscheulich1022]

單純只是因為乘3後+1恰巧是完全平方數吧（？

[@SundayTetris]

可能是題目有設計好就是要這麼算的？

[@ChinaziXitler]

不是巧合，題目就是設計這樣算的，否則沒辦法快速解開

[@weirenwang9100]

这不就是小时候学的配方法嘛。。多练习练习一眼应该能看出来吧

[@tsai-8366]

573489999 質因數分解。

[@xl3048]

3就能整除哈哈哈哈😂😂😂

[@MsSanze]

83333=19*19*23 按試除法解之較快。

[@henrylin1498]

19*19*23=8303

[@李芬迪]

算錯

[@MsSanze]

83333=19*19*23

[@fanye682]

=83303

[@猩猩www7305]

有講跟沒講一樣…

[@李龍馨]

他說的不錯啊

[@一二三-m4u]

@@李龍馨 對啊我也覺得不錯

[@nightsharkski]

那您来分享一下更好的更快的方法啦 光说不练打嘴炮您很厉害哦

[@hakkiwong3155]

我也觉得很不错啊

[@nelson723]

期待您有更快的解法分享