線上積分：http://integrals.wolfram.com/index.jsp

所以當時我都會直接把這些值背下來，

也因此現在對它的記憶就只剩下 0, 1, 1, 0, 0, -1, -1, 0 了。

國小一直處在普通階段，只有比別人會算雞兔同籠問題。

國中始終搞不懂時針分針重疊的問題，但是知道一天 24 小時這兩者只會重疊 22 次。

高中只拿過一次數學 100 分，而同一次段考拿 100 的都已經是博士了。

大學成績頗差，又沒有一技之長，只得考比較少人的數學所來緩徵。

研究所做的東西是在跑操場時想出來的，所以也沒什麼了不起，只有在找工作面試時可以拖時間。

Let A = , we can rewrite A as .

Since and , then A.

Let B = , since , then A<B.

Thus , that is

解答：Suppose we have know that

For every integer , then or mod 4.

Then or mod 4.

So is not an integer

解答：[1001/5] + [1001/25] + [1001/125] + [1001/625] = 200 + 40 + 8 + 1 = 249

, where [] means floor function

解答：Suppose we have know that

For every integer which is not divisible by 7, then or mod 7.

Assume are not divisible by 7, then or mod 7.

However or mod 7, then mod 7.

That means is divisible by 7.

解答：Suppose we have know the following lemma

If is prime, then is divisible by if and only if nonnegative integer

For convenience, let and , where is also an integer.

Then we can rewrite as

Since is an integer, then is divisible by .

Thus is also divisible by , since is prime.

Then is divisible by ,

and is also divisible by since .

Hence is divisible by , that means is an integer

定理證明了四色經典的方式由俄羅斯數學家 Gorbatov V. A. 1964。短版證明（高達 1頁）Chechulin V. L. 2006年發表。(http://www.uresearch.psu.ru/files/articles/17_89592.doc)

對四色定理有莫名偏執的我馬上點了連結，不過連結失效。而我用 『17_89592.doc』 Google 過後發現只有少數幾個連結，然後在這裡透過 Google 翻譯，我大概猜出上面這件事情應該是有個叫 Gorbatov V. A. 的數學家在 1964 年證明出四色定理(就目前已知的情況來說他的證明是錯的)，然後 Chechulin V. L. 在 2006 年把它簡化然後重新投稿到某個期刊上，結果被接受了。接著維基百科【四色定理】就被加了這段文章。

BTW 現在又多我一個網頁有這個連結了。