Maths Divisible Question ? (Urgent)

Explanation as follows:

圖片參考：http://i238.photobucket.com/albums/ff245/chocolate328154/Maths514.jpg?t=1223716734


2008-10-12 12:52:47 補充：
Thank you for your suggestion. I will think over it...

2008-10-14 19:03:49 補充：
I have retyped my proof, plx press reload for it =]

To jeanhim，Copestone既證明係based on a^3|b^3呢個前提，而你呢個例子並不乎合呢個前提。

不明這一句：「我們證明了任意質數 p|a 必有 p|b, 所以 a|b。 」

2 | 4 2 | 6 so 4 | 6 ??

既然要完全從基本出發，那麼 M must be a cubic root 有跳步，並不明顯。

2008-10-15 00:02:51 補充：
啊，我真白目，謝。今次錯不了。
By assumption, for some k, ka^3 = b^3.

Let GCD(a, b) = m. Then a = mc and b = md
and so kc^3 = d^3, where GCD(c, d) = 1
But then c | d^3, GCD(c, d) = 1 would imply that c = 1, and so k = d^3. As a result, da = b and so a | b. We are done.

2008-10-15 11:42:25 補充：
對不起，原先的有點亂來，不好意思。其實最重要的一步是把 a 及 b 的共同因子完全約掉，那麼剩下的因子就必定互質，就可以輕易得出結論了。