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On the irreducibility of the iterates of $x^{n}-b$


Authors: Lynda Danielson and Burton Fein
Journal: Proc. Amer. Math. Soc. 130 (2002), 1589-1596
MSC (2000): Primary 12E05; Secondary 11D41
DOI: https://doi.org/10.1090/S0002-9939-01-06258-X
Published electronically: October 17, 2001
MathSciNet review: 1887002
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Abstract: Let $K$ be a field and suppose that $f(x)=x^{n}-b$ is irreducible in $K[x]$. We discuss the following question: under what conditions are all iterates of $f$ irreducible over $K$?


References [Enhancements On Off] (What's this?)

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Additional Information

Lynda Danielson
Affiliation: Department of Mathematics, Albertson College of Idaho, Caldwell, Idaho 83605
Email: ldanielson@albertson.edu

Burton Fein
Affiliation: Department of Mathematics, Oregon State University, Corvallis, Oregon 97331
Email: fein@math.orst.edu

DOI: https://doi.org/10.1090/S0002-9939-01-06258-X
Keywords: Iterated polynomial, irreducible, generalized Fermat equation, $abc$-conjecture
Received by editor(s): April 13, 2000
Received by editor(s) in revised form: December 20, 2000
Published electronically: October 17, 2001
Additional Notes: The second author is grateful for support under NSA Grant MDA904-97-1-0040
Communicated by: Lance W. Small
Article copyright: © Copyright 2001 American Mathematical Society

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