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How to check whether a positive integer can be written as linear combination of given others, where all coefficients are positive?

Let $n$, $k$ and $m_1, \dots, m_k$ be positive integers. Which is the most efficient algorithm to find out whether there are positive integers $a_1, \dots, a_k$ such that $n = \sum_{i=1}^k a_i m_i$? ...
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