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27 elements

Source: Unirea contest, 2003

April 22, 2006
algebrapolynomialabstract algebrasuperior algebrasuperior algebra unsolved

Problem Statement

Let K\displaystyle \mathcal K be a field with 27\displaystyle 27 elements. Prove that there is aāˆˆK\displaystyle a \in \mathcal K such that a3=a+2\displaystyle a^3 = a + 2. Mircea Becheanu
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