Olympiad Problem 7

Algebra Level 5

Find the sum of all positive integers \(n,k_1, k_2, \ldots , k_n\) such that \( \displaystyle \sum_{m=1}^n k_m = 5n - 4\) and \(\displaystyle \sum_{m=1}^n \dfrac1{k_m} = 1 \).

Note: The order of \(k_i\) do not matter.

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