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Canadian Number Theory Association X Meeting (CNTA X)
July 13-18, 2008
University of Waterloo
Waterloo, Ontario, Canada

Organizers
Kevin Hare (Waterloo, Wentang Kuo (Waterloo), Yu-Ru Liu (Waterloo), David McKinnon (Waterloo), Michael Rubinstein (Waterloo), Cam Stewart (Waterloo)

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Rational-Derived Polynomials
by
Jim MacDougall
University of Newcastle (Australia)
Coauthors: R. H. Buchholz

A polynomial p in ℚ[x] is called rational-derived if all of its roots are

rational and all the roots of all of its derivatives are rational. All

such polynomials of degree 3 are easily characterized. Surprisingly,

already at degree 4 we do not know how to describe all such polynomials.

In particular no rational-derived polynomial with 4 distinct roots has

been found. This talk will survey what is known about this and some

related problems.

Date received: May 5, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawl-39.