find (a,b)
$a,b\epsilon N$ and $ 2ab-1,$ divides\[(4a^2-1)^2,\]find all $(a,b)$
Re: find (a,b)
The famous IMO 2007.
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Re: find (a,b)
Vieta Jumping.....?? i cant understand....plz give me ful solutn
- FahimFerdous
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- Location:Mymensingh, Bangladesh
Re: find (a,b)
I can't understand the problem. Is it find (a,b) such that (2ab-1) divided (4a^2-1)^2?
Your hot head might dominate your good heart!
- FahimFerdous
- Posts:176
- Joined:Thu Dec 09, 2010 12:50 am
- Location:Mymensingh, Bangladesh
Re: find (a,b)
I can't understand the problem. Is it find (a,b) such that (2ab-1) divides (4a^2-1)^2?
Your hot head might dominate your good heart!
Re: find (a,b)
$4a^2-1$ is odd number, so $(4a^2-1)^2$ is odd number. It gives 2 divides an odd number. Impossible. no solution for $(a,b)$
A man is not finished when he's defeated, he's finished when he quits.
- Tahmid Hasan
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Re: find (a,b)
shit. I again do wron. I saw $2ab$ instead of $2ab-1$. Trying again. But what happend with my eye! I am reading problem foolishly!Tahmid Hasan wrote:hasib, let's input $b=1$ and $a=any natural number$
A man is not finished when he's defeated, he's finished when he quits.
- Tahmid Hasan
- Posts:665
- Joined:Thu Dec 09, 2010 5:34 pm
- Location:Khulna,Bangladesh.
Re: find (a,b)
n prob,i have proved that there are infinite solns,will thaaat give me som marks????????
বড় ভালবাসি তোমায়,মা
Re: find (a,b)
wel done....tahmid....bt theres missing infinite solutins