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Austria-Poland where the sum is 27 and the product 24

Source: Austria-Poland 2004, single competition, problem 5

February 13, 2005
inductionanalytic geometryalgebra unsolvedalgebra

Problem Statement

Determine all nn for which the system with of equations can be solved in R\mathbb{R}: ∑k=1nxk=27\sum^{n}_{k=1} x_k = 27 and ∏k=1nxk=(32)24.\prod^{n}_{k=1} x_k = \left( \frac{3}{2} \right)^{24}.
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