Imo 2007-5

Discussion on International Mathematical Olympiad (IMO)
tarek like math
Posts:56
Joined:Fri Feb 18, 2011 11:30 pm
Re: Imo 2007-5

Unread post by tarek like math » Sat May 07, 2011 10:40 pm

then d is divisor of $4ab-4a^2$ and if d don't accept 4 as a value then d is factor of a. my request try to understand that then u find a contradiction.

User avatar
Masum
Posts:592
Joined:Tue Dec 07, 2010 1:12 pm
Location:Dhaka,Bangladesh

Re: Imo 2007-5

Unread post by Masum » Sun May 08, 2011 11:27 am

Uhh. What about $d=7,a=3,b=10$?
Then $7|4*10*3-1$ and $7|4*3^2-1$ and $7|4*10^2-1$ and $7|10-3=a-b$ and $7$ does not divide $10$ or $3$. So, I can't find any contradiction!
One one thing is neutral in the universe, that is $0$.

tarek like math
Posts:56
Joined:Fri Feb 18, 2011 11:30 pm

Re: Imo 2007-5

Unread post by tarek like math » Mon May 09, 2011 2:37 am

sadly u r right! but i find my mistake, $d$ divisor of $4a^2-1,4ab-1$ and $4ab-4a^2$,it doesn't means $d$ factor of both $4ab$ and $4a^2$ but $d$ divisor of $4ab-1$ and $4a^2-1$ actually $d$ factor of $4a(b-a)$ then since $4a$ not divide $A,B$ so $d=(b-a)$ [here b>a]. thanks for ur kind reply but u can feel happy for that at least u make someone understand.
$d=(b-a)$,i will try to prove it from here.thank u.

User avatar
Masum
Posts:592
Joined:Tue Dec 07, 2010 1:12 pm
Location:Dhaka,Bangladesh

Re: Imo 2007-5

Unread post by Masum » Mon May 09, 2011 2:21 pm

tarek like math wrote:sadly u r right! but i find my mistake, $d$ divisor of $4a^2-1,4ab-1$ and $4ab-4a^2$,it doesn't means $d$ factor of both $4ab$ and $4a^2$ but $d$ divisor of $4ab-1$ and $4a^2-1$ actually $d$ factor of $4a(b-a)$ then since $4a$ not divide $A,B$ so $d=(b-a)$ [here b>a]. thanks for ur kind reply but u can feel happy for that at least u make someone understand.
$d=(b-a)$,i will try to prove it from here.thank u.
Still that's wrong. This doesn't mean that $d=a-b$, only $d|a-b$.
One one thing is neutral in the universe, that is $0$.

tarek like math
Posts:56
Joined:Fri Feb 18, 2011 11:30 pm

Re: Imo 2007-5

Unread post by tarek like math » Wed May 11, 2011 5:20 pm

oh, it's a mistake but in previous line i say $d$ factor of $4a(b-a)$ then i missed it.

User avatar
Masum
Posts:592
Joined:Tue Dec 07, 2010 1:12 pm
Location:Dhaka,Bangladesh

Re: Imo 2007-5

Unread post by Masum » Fri May 13, 2011 11:15 pm

But I think it would be a better suggestion for you that don't try a problem from only one fixed view. Because your approach might be wrong.
One one thing is neutral in the universe, that is $0$.

Post Reply