A binomial-like matrix equation

Abstract : We show that a pair of matrices satisfying a certain algebraic identity, reminiscent of the binomial theorem, must have the same characteristic polynomial. This is a generalization of Problem 4 (11th grade) from the Romanian National Mathematical Olympiad 2011.
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Alin Bostan, Thierry Combot. A binomial-like matrix equation. American Mathematical Monthly, Mathematical Association of America, 2012, 119 (7), pp.593-597. ⟨10.4169/amer.math.monthly.119.07.593⟩. ⟨hal-00780438⟩

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