IMO Shortlist 2013 problem N2


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Dodao/la: arhiva
21. rujna 2014.
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Prove that for any pair of positive integers k and n there exist k positive integers m_1, m_2, \ldots, m_k such that 
  1 + \frac{2^k - 1}{n} =
    \left( 1 + \frac{1}{m_1} \right)
    \left( 1 + \frac{1}{m_2} \right)
    \cdots
    \left( 1 + \frac{1}{m_k} \right) \text{.}
Izvor: Japan