Spring 2016, problem 10
Find all pairwise relatively prime positive integers $l, m, n$ such that $$(l+m+n)\left( \frac{1}{l}+\frac{1}{m}+\frac{1}{n}\right)$$ is an integer.
Find all pairwise relatively prime positive integers $l, m, n$ such that $$(l+m+n)\left( \frac{1}{l}+\frac{1}{m}+\frac{1}{n}\right)$$ is an integer.