Value sets of functions over finite fields

Stephen Cohen

Displaying similar documents to “Value sets of functions over finite fields”

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....

Integration of some very elementary functions

Jan Mařík (1993)

Mathematica Bohemica

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Let $m$ be a natural number. Let $f, g$ and $Q$ be real polynomials such that ${d e g f, d e g g} \subset {1, 2}, d e g Q < m d e g f, g$ is not a square and $f$ has imaginary roots, if it is not linear. Effective methods for the integration of $Q / (f^{m} \sqrt{g}$ are exhibited.