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ℚ-derived

Proceedings of the Edinburgh Mathematical Society (1)

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ON ℚ-DERIVED POLYNOMIALS
E. V. Flynn
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 44 / Issue 1 / February 2001

Published online by Cambridge University Press:

20 January 2009, pp. 103-110
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It is known that ℚ-derived univariate polynomials (polynomials defined over ℚ, with the property that they and all their derivatives have all their roots in ℚ) can be completely classified subject to two conjectures: that no quartic with four distinct roots is ℚ-derived, and that no quintic with a triple root and two other distinct roots is ℚ-derived. We prove the second of these conjectures.
AMS 2000 Mathematics subject classification: Primary 11G30