Dhaka Higher Secondary 2010/8
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Please don't post problems (by starting a topic) in the "Higher 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.
Please don't post problems (by starting a topic) in the "Higher 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.
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 $P$?
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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.
long way to go .....
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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