APMO 2004
Prove that
$\left\lfloor \frac{(n-1)!}{n(n+1)}\right\rfloor$
is even for every positive integer $n$.
$\left\lfloor \frac{(n-1)!}{n(n+1)}\right\rfloor$
is even for every positive integer $n$.
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- zadid xcalibured
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Re: APMO 2004
we can demonstrate two cases.one of n and n+1 is prime.then the other case is both of them are composite.im not done with the second case.
Re: APMO 2004
It is quite easy(and quite cool ).
My solution scheme:
My solution scheme:
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Nur Muhammad Shafiullah | Mahi
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- Phlembac Adib Hasan
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Re: APMO 2004
Very easy.I also solved this in national camp (while watching the exciting game of India vs Bangladesh. )
Last edited by Phlembac Adib Hasan on Thu Mar 29, 2012 11:27 am, edited 1 time in total.
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- FahimFerdous
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Re: APMO 2004
A classic one! I solved it too during National Camp, with regards to Mahi who gave me a hint.
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- Phlembac Adib Hasan
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Re: APMO 2004
*Mahi* Vaia wrote:Step 3. : For none of $n,n+1$ prime , prove $n \text { and } n+1 | (n-1)!$ for "sufficiently large" $n$.
"sufficiently large" শুনতেই বিশাল বিশাল সংখ্যার কথা মনে হচ্ছে।আসলে $n\ge 8$ নিলেই হয়।
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Re: APMO 2004
Yeah, and that's why I used the wink .Phlembac Adib Hasan wrote:*Mahi* Vaia wrote:Step 3. : For none of $n,n+1$ prime , prove $n \text { and } n+1 | (n-1)!$ for "sufficiently large" $n$.
"sufficiently large" শুনতেই বিশাল বিশাল সংখ্যার কথা মনে হচ্ছে।আসলে $n\ge 8$ নিলেই হয়।
Please read Forum Guide and Rules before you post.
Use $L^AT_EX$, It makes our work a lot easier!
Nur Muhammad Shafiullah | Mahi
Use $L^AT_EX$, It makes our work a lot easier!
Nur Muhammad Shafiullah | Mahi