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

Author(s): Lynda Danielson; Burton Fein
Journal: Proc. Amer. Math. Soc. 130 (2002), 1589-1596.
MSC (2000): Primary 12E05; Secondary 11D41
Posted: October 17, 2001
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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 $K$?

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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: 10.1090/S0002-9939-01-06258-X
PII: S 0002-9939(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
Posted: October 17, 2001
Additional Notes: The second author is grateful for support under NSA Grant MDA904-97-1-0040
Communicated by: Lance W. Small
Copyright of article: Copyright 2001, American Mathematical Society

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