IMO 1979

Discussion on International Mathematical Olympiad (IMO)
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SANZEED
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IMO 1979

Unread post by SANZEED » Sun May 20, 2012 1:23 am

Let \[p,q\in \mathbb{N}\]
such that
\[\frac{p}{q}=1-\frac{1}{2}+\frac{1}{3}-....-\frac{1}{1318}+\frac{1}{1319}\]
Prove that \[1979\] divides $p$.
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User avatar
SANZEED
Posts:550
Joined:Wed Dec 28, 2011 6:45 pm
Location:Mymensingh, Bangladesh

Re: IMO 1979

Unread post by SANZEED » Sat Jun 02, 2012 12:16 am

Well,my solution should be this...
we will use the Catalan identity:
$1-\frac{1}{2}+\frac{1}{3}-......-\frac{1}{2n}=\frac{1}{n+1}+\frac{1}{n+2}+.....+\frac{1}{2n}$
This will yield the result.
$\color{blue}{\textit{To}} \color{red}{\textit{ problems }} \color{blue}{\textit{I am encountering with-}} \color{green}{\textit{AVADA KEDAVRA!}}$

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