Olympiad Questions Here !!!

I'm deeply sorry Orange for lacking you with the questions in your forum and your Vit C. Sorry...
So I gladly type it all here ya...
Er, I will be skipping some questions ya... But try solving these first lar...

Starting from 1998,
1. Given x and y is positive odd integer, prove that x² + y² cannot form a perfect square.

2. In a triangle ABC, the values of tan A, tan B, tan C is equal to the ratio of 1:2:3. Find the ration of length AC to length AB

3. A function, f has the property of f(1) + f(2) + ... + f(n) = n²f(n) for each positive integer of n. Given f(1) = 1999, find f(1998)

5. Show that there is no positive integer (x, y. z), that is the solution to 3x + 4x = 5x, besides from (2, 2, 2).


Year 1999
1. If a² + b² = 1 and c² + d² = 1, show that (ac+bd)² ≤ 1



Due to my laziness, please visit http://cage.rug.ac.be/~hvernaev/olympiad.html for all the olympiad questions... THANK YOU!@!!
you people are taking The Asian Pacific Math Olympiad.