Question 60
Prove that for every pair of positive integers k and n there exist k positive integers $m_1,m_2,\ldots,m_k$ (not necessarily distinct) such that
$$1+\frac{2^k-1}{n}=\left(1+\frac1{m_1}\right)\left(1+\frac1{m_2}\right)\cdots\left(1+\frac1{m_k}\right).$$
$$1+\frac{2^k-1}{n}=\left(1+\frac1{m_1}\right)\left(1+\frac1{m_2}\right)\cdots\left(1+\frac1{m_k}\right).$$