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MathNet 2014 Question 25

Math Olympiad Vault · MathNet 2014

Question 25

Find all positive integers $n\gt 1$ with the following property:
for each two positive divisors $k, \ell\lt n$ of $n$, at least one of the numbers $2 k-\ell$ and $2 \ell-k$ is a (not necessarily positive) divisor of $n$ as well.