I have a question that I've been thinking for a while now.
Can you find a set of distinct positive odd integers $n_1, n_2, \ldots, n_k$ for some finite positive integer $k$ such that $\left(\frac{1}{n_1} + \frac{1}{n_2} + \ldots + \frac{1}{n_k} \right)$ is a positive integer as well?
This statement obviously holds if we allow $n_1 \ldots n_k$ to be even. I'd be glad if you can recommend some articles that study this particular problem.