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Displaying similar documents to “Some properties of the ring of Nash functions”

Irreducibility of the iterates of a quadratic polynomial over a field

Mohamed Ayad, Donald L. McQuillan (2000)

Acta Arithmetica

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1. Introduction. Let K be a field of characteristic p ≥ 0 and let f(X) be a polynomial of degree at least two with coefficients in K. We set f₁(X) = f(X) and define f r + 1 ( X ) = f ( f r ( X ) ) for all r ≥ 1. Following R. W. K. Odoni [7], we say that f is stable over K if f r ( X ) is irreducible over K for every r ≥ 1. In [6] the same author proved that the polynomial f(X) = X² - X + 1 is stable over ℚ. He wrote in [7] that the proof given there is quite difficult and it would be of interest to have an elementary proof....