| Mircea Crasmareanu†
Abstract: The purpose of this paper is to introduce and examine two classes of quartic real polynomials P having the same Euclidean norm as their Lagrange resolvent, respectively, having the square of the Euclidean norm equal to the height of the Lagrange resolvent. The reduced form of the polynomial P is provided, which eliminates the cubic term. Find ing such polynomials with integer coefficients is always of interest. The Lagrange resolvent associates a cubic curve with each of these polynomials as a cubic polynomial. It highlights the situations in which these cubic curves are elliptic curves. Keywords: quartic real polynomial, Lagrange resolvent, Euclidean-Lagrange polynomial, cubic curve, Cantor-Lagrange polynomial. MSC: 12D05, 51N35, 65H04. DOI 10.56082/annalsarscimath.2026.2.103 †mcrasm@uaic.ro, Faculty of Mathematics, Alexandru Ioan Cuza University, Iasi, 700506, Romania |
PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics and Its Application,
ISSN ONLINE 2066 – 6594
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