數學難題(數學高手入)

This is a very interesting question, and in order to prove this, you have to use a method called "contradiction". This is attributed by "Euclid".

The theroy of "Method of Contradiction" is defined as like this:

You try to agree something. Then, you first assume you don't agree and then you work on it until you reach a contradiction (dead end). Then finally, it seems like it cannot be disagreed.

So, back to the prove of 質數有無限多個...

Assume that 質數是有限的 and all of them are listed as: p1, p2 ..., pn.

Consider the number Q = p1 乘 p2 乘 p3 乘 p4... pn 1 and the number Q is either 質數 or 非質數. If Q 除 p1 or p2 or p3...如始類推, then the result will have a reminder of 1.

所以Q是一個質數, 與此同時, Q這個質數是不包括在p1, p2, p3 ...到pn.

所以 this mathematical proves reach to a contradiction. 推翻了之前的assumption. Therefore 質數是無限的.

2008-12-02 14:59:32 補充：
我打少左個加(+)號 ....... the number Q = p1 乘 p2 乘 p3 乘 p4... pn + 1 and the number Q is either......

數字是有無限大;
質數也是數字的一種;
所以質數也有無限多個.

你想知就一定要搵哪個乜乜term,可惜i don't know(我中一時搵了很久都搵不到!)