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Generalization of a RMO-2012 problem

A similar problem was given in three different regions in RMO(just the values were bit altered).I am giving it's generalization.Prove it.-

Suppose \(x_{0},x_{1},..,x_{n}\) are natural numbers such that \(x_{0}|x_{1}^{m}\), \(x_{1}|x_{2}^{m}\),...,\(x_{n}|x_{0}^{m}\) where \(m≥1\) is a natural number.

Then show that \(∏_{i=0}^{n}x_{i}|(\sum_{i=0}^{n}x_{i})^{\frac{m^{n+1}-1}{m-1}}\).

Note by Souryajit Roy
3 years ago

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