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IMO 2013 NO 1

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Buktikan bahwa untuk sebarang pasangan bilangan bulat $k$ dan $n$, terdapat $k$ bilangan bulat positif $m_1$, $m_2$, ... , $m_k$ (tidak harus berbeda) sehingga 


$1+\displaystyle \frac{2^k-1}{n} = \displaystyle\prod\limits_{i=1}^k \left( 1 + \frac{1}{m_i} \right)$

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