Dhaka Secondary 2010/6

Problem for Secondary Group from Divisional Mathematical Olympiad will be solved here.
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BdMO
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Dhaka Secondary 2010/6

Unread post by BdMO » Fri Jan 21, 2011 7:06 pm

For how many prime numbers $N$ for which $N+1$ is a perfect square.

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leonardo shawon
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Re: Dhaka Secondary 2010/6

Unread post by leonardo shawon » Tue Jan 25, 2011 12:59 pm

1..


May be!!!!!!
Ibtehaz Shawon
BRAC University.

long way to go .....

Sudip Deb
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Re: Dhaka Secondary 2010/6

Unread post by Sudip Deb » Tue Jan 25, 2011 7:10 pm

There is an only number which is 3 and 3+1 is a sqare . :-)

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leonardo shawon
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Re: Dhaka Secondary 2010/6

Unread post by leonardo shawon » Tue Jan 25, 2011 9:09 pm

actually the question was HOW Many Numbers! So i wrote the answer.. Thats there r 1 number.
and yes. Only number is 3. And 3+1=4 is a perfect square number.
Ibtehaz Shawon
BRAC University.

long way to go .....

Sudip Deb new
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Re: Dhaka Secondary 2010/6

Unread post by Sudip Deb new » Wed Jan 26, 2011 10:04 am

Yaap . Ami bistarito vabe bollam .

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Zzzz
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Re: Dhaka Secondary 2010/6

Unread post by Zzzz » Thu Jan 27, 2011 10:27 am

We should prove that 3 is only such prime.

If $N+1=k^2$ then $N=k^2-1 \Rightarrow N=(k-1)(k+1)$ as $N$ is prime, $k-1=1\ \ \therefore k=2$
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leonardo shawon
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Re: Dhaka Secondary 2010/6

Unread post by leonardo shawon » Thu Jan 27, 2011 1:29 pm

Zzzz wrote:We should prove that 3 is only such prime.

If $N+1=k^2$ then $N=k^2-1 \Rightarrow N=(k-1)(k+1)$ as $N$ is prime, $k-1=1\ \ \therefore k=2$
how did it become?
$(k-1)(k+1)=N as N is a prime, so (k-1)=1 . . . ?
Ibtehaz Shawon
BRAC University.

long way to go .....

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Zzzz
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Re: Dhaka Secondary 2010/6

Unread post by Zzzz » Thu Jan 27, 2011 1:34 pm

leonardo shawon wrote:
Zzzz wrote:We should prove that 3 is only such prime.

If $N+1=k^2$ then $N=k^2-1 \Rightarrow N=(k-1)(k+1)$ as $N$ is prime, $k-1=1\ \ \therefore k=2$
how did it become?
$(k-1)(k+1)=N as N is a prime, so (k-1)=1 . . . ?
k+1 and k-1 both are factors of a prime number. Each prime number has only two factors - 1 and the prime itself. So k-1=1.
Every logical solution to a problem has its own beauty.
(Important: Please make sure that you have read about the Rules, Posting Permissions and Forum Language)

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