Dhaka Secondary 2010/6

[BdMO]

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

[leonardo shawon]

1..


May be!!!!!!

[Sudip Deb]

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

[leonardo shawon]

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.

[Sudip Deb new]

Yaap . Ami bistarito vabe bollam .

[Zzzz]

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, $k-1=1\ \ \therefore k=2$

[leonardo shawon]

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 . . . ?

[Zzzz]

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.