National Secondary 2010/10

Discussion on Bangladesh Mathematical Olympiad (BdMO) National
Post Reply
User avatar
Fatin Farhan
Posts:75
Joined:Sun Mar 17, 2013 5:19 pm
Location:Kushtia,Bangladesh.
Contact:
Contact Fatin Farhan
National Secondary 2010/10

Unread post by Fatin Farhan » Sun Feb 09, 2014 3:48 pm

In a set of $$131$$ natural numbers, no number has a prime factor greater than $$42$$. Prove that it
is possible to choose four numbers from this set such that their product is a perfect square.
"The box said 'Requires Windows XP or better'. So I installed L$$i$$nux...:p"
Top
User avatar
*Mahi*
Posts:1175
Joined:Wed Dec 29, 2010 12:46 pm
Location:23.786228,90.354974
Contact:
Contact *Mahi*

Re: National Secondary 2010/10

Unread post by *Mahi* » Sun Feb 09, 2014 11:14 pm

Hint:
Consider the numbers as prime powers, with powers modulo $2$
There are $2^{13}$ possible arrangements of those powers, and $\binom {129}{2}$ unique pairs of powers, as $2^{13} < \binom {129}{2}$ we are done(why?)

Because we are done when we get two unique pairs with same power combination.(again, why?)
Check the edges carefully, they can be rough.
Please read Forum Guide and Rules before you post.

Use $L^AT_EX$, It makes our work a lot easier!

Nur Muhammad Shafiullah | Mahi
Top
Post Reply

Return to “National Math Olympiad (BdMO)”