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2013 IMO Problems/Problem 1

Revision as of 00:34, 11 October 2013 by DANCH (talk | contribs) (Created page with "==Problem== Prove that for any pair of positive integers <math>k</math> and <math>n</math>, there exist <math>k</math> positive integers <math>m_1,m_2,...,m_k</math> (not necessa...")
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Problem

Prove that for any pair of positive integers $k$ and $n$, there exist $k$ positive integers $m_1,m_2,...,m_k$ (not necessarily different) such that

$1+\frac{2^k-1}{n}=(1+\frac{1}{m_1})(1+\frac{1}{m_2})...(1+\frac{1}{m_k})$.

Solution

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See Also

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