Školjka

%V0 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 $$ 1 + \frac{2^k - 1}{n} = \left( 1 + \frac{1}{m_1} \right) \left( 1 + \frac{1}{m_2} \right) \cdots \left( 1 + \frac{1}{m_k} \right) \text{.} $$