ON ℚ-DERIVED POLYNOMIALS
E. V. Flynn · Proceedings of the Edinburgh Mathematical Society · 2001
Abstract 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