Dhaka Higher Secondary 2010/8

Problem for Higher Secondary Group from Divisional Mathematical Olympiad will be solved here.
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BdMO
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Dhaka Higher Secondary 2010/8

Unread post by BdMO » Tue Jan 18, 2011 2:06 pm

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
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Re: Dhaka Higher Secondary 2010/8

Unread post by leonardo shawon » Tue Jan 18, 2011 6:40 pm

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 .....

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Moon
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Re: Dhaka Higher Secondary 2010/8

Unread post by Moon » Tue Jan 18, 2011 7:19 pm

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, $P=2,4,8.$
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