Imo 1959-1

Discussion on International Mathematical Olympiad (IMO)
User avatar
Masum
Posts:592
Joined:Tue Dec 07, 2010 1:12 pm
Location:Dhaka,Bangladesh
Imo 1959-1

Unread post by Masum » Thu Dec 09, 2010 8:29 pm

Prove that the fraction $\dfrac {21n+4} {14n+3}$ is irreducible.
Last edited by Moon on Sat Dec 11, 2010 9:21 pm, edited 3 times in total.
Reason: use \dfrac {21n+4} {14n+3} for larger fractions.
One one thing is neutral in the universe, that is $0$.

ishfaqhaque
Posts:20
Joined:Thu Dec 09, 2010 3:30 pm

Re: Imo 1959-1

Unread post by ishfaqhaque » Wed Jan 05, 2011 1:15 pm

Use $ax+by=1$ implies a and b coprime for integer $a, b, x,y $

sourav das
Posts:461
Joined:Wed Dec 15, 2010 10:05 am
Location:Dhaka
Contact:

Re: Imo 1959-1

Unread post by sourav das » Tue May 17, 2011 4:32 pm

Let $(21n + 4, 14n + 3) = p$
So, $p/ 3 * (14n + 3) - 2 * (21n + 4) = 1$

(proved)
You spin my head right round right round,
When you go down, when you go down down......
(-$from$ "$THE$ $UGLY$ $TRUTH$" )

User avatar
Tahmid Hasan
Posts:665
Joined:Thu Dec 09, 2010 5:34 pm
Location:Khulna,Bangladesh.

Re: Imo 1959-1

Unread post by Tahmid Hasan » Tue May 17, 2011 4:47 pm

euclidean algorithm can also be used to solve this problem.
বড় ভালবাসি তোমায়,মা

Post Reply