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MathNet 2013 Question 82

Math Olympiad Vault · MathNet 2013

Question 82

Let $n$ be a composite positive integer and let $d_1, d_2, \dots, d_m$ be all of its divisors. Prove that the following equation holds:
$$
\frac{2}{\log n^m} \sum_{k=1}^{m} \log d_k = 1.
$$