## Dhaka Secondary 2010/6

Problem for Secondary Group from Divisional Mathematical Olympiad will be solved here.
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Please don't post problems (by starting a topic) in the "Secondary: Solved" forum. This forum is only for showcasing the problems for the convenience of the users. You can post the problems in the main Divisional Math Olympiad forum. Later we shall move that topic with proper formatting, and post in the resource section.
BdMO
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### Dhaka Secondary 2010/6

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

leonardo shawon
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Location: Dhaka

### Re: Dhaka Secondary 2010/6

1..

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

long way to go .....

Sudip Deb
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### Re: Dhaka Secondary 2010/6

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

leonardo shawon
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Location: Dhaka

### Re: Dhaka Secondary 2010/6

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

Yaap . Ami bistarito vabe bollam .

Zzzz
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### Re: Dhaka Secondary 2010/6

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\$
Every logical solution to a problem has its own beauty.
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leonardo shawon
Posts: 169
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Location: Dhaka

### Re: Dhaka Secondary 2010/6

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 .....

Zzzz
Posts: 172
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Location: 22° 48' 0" N / 89° 33' 0" E

### Re: Dhaka Secondary 2010/6

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)