## Dhaka Higher Secondary 2010/8

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### Dhaka Higher Secondary 2010/8

If $N$ and $P$ are integers greater than $1$ and if $P$ is a factor of both $N+4$ and $N+12$, what are the values of $P$?

- leonardo shawon
**Posts:**169**Joined:**Sat Jan 01, 2011 4:59 pm**Location:**Dhaka

### Re: Dhaka Higher Secondary 2010/8

for all Positive Ivan numbers [ >1] , (n+4) and (n+12) will be Ivan. And P will be their factor if P=2.

Ibtehaz Shawon

BRAC University.

BRAC University.

*long way to go .....*### Re: Dhaka Higher Secondary 2010/8

I thing you meant even number (জোড় সংখ্যা) by "ivan". BTW you can not just choose a random number; you have to prove it for general case.

As $P$ divide $N+4$ and $N+12$, $P | (N+12)-(N+4)$ i.e. $P|8$. So the factors of $8$ are the values of $P$. So, $P=2,4,8.$

As $P$ divide $N+4$ and $N+12$, $P | (N+12)-(N+4)$ i.e. $P|8$. So the factors of $8$ are the values of $P$. So, $P=2,4,8.$

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