find (a,b)

faisalnir · Unread post by **faisalnir** » Tue Feb 01, 2011 2:39 am

$a,b\epsilon N$ and $ 2ab-1,$ divides\[(4a^2-1)^2,\]find all $(a,b)$

Unread post by **Moon** » Tue Feb 01, 2011 8:53 am

The famous IMO 2007.

faisalnir · Unread post by **faisalnir** » Tue Feb 01, 2011 12:32 pm

Vieta Jumping.....?? i cant understand....plz give me ful solutn

FahimFerdous · Unread post by **FahimFerdous** » Tue Feb 01, 2011 2:59 pm

I can't understand the problem. Is it find (a,b) such that (2ab-1) divided (4a^2-1)^2?

FahimFerdous · Unread post by **FahimFerdous** » Tue Feb 01, 2011 2:59 pm

I can't understand the problem. Is it find (a,b) such that (2ab-1) divides (4a^2-1)^2?

Hasib · Unread post by **Hasib** » Tue Feb 01, 2011 4:41 pm

$4a^2-1$ is odd number, so $(4a^2-1)^2$ is odd number. It gives 2 divides an odd number. Impossible.

no solution for $(a,b)$

Tahmid Hasan · Unread post by **Tahmid Hasan** » Tue Feb 01, 2011 6:22 pm

hasib, let's input $b=1$ and $a=any natural number$

Hasib · Unread post by **Hasib** » Tue Feb 01, 2011 6:30 pm

Tahmid Hasan wrote:hasib, let's input $b=1$ and $a=any natural number$

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 · Unread post by **Tahmid Hasan** » Tue Feb 01, 2011 6:55 pm

n prob,i have proved that there are infinite solns,will thaaat give me som marks????????

faisalnir · Unread post by **faisalnir** » Tue Feb 01, 2011 8:54 pm

wel done....tahmid....bt theres missing infinite solutins

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