Exist or does not exist

Is giving hints a good way to help students in solving mathematics problems? Urm, sometimes it may not.

Here is a common m.i. question in recent F.4 additional mathematics regular test:

Show that is divisible by 3 for any positive integer .

不能秒殺的提問

在堂上，一般情況下，學生提問，在下多半手起刀落，秒殺解之。今天 4E 同學問了兩個問題，在下不能秒殺：

1. 誰發明 這個符號？
2. 畢氏數組中是否必然存在 3 或 5 的倍數？