Quartic polynomials with a given discriminant
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Date
2022-02-21
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Mark
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De Gruyter
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Abstract
Let $ 0\ne D \in \Bbb Z$ and let $Q_D$ be the set of all monic quartic polynomials $ x^4 +ax^3 +bx^2 + cx + d \in \Bbb Z[x]$ with the discriminant equal to $D$. In this paper we will devise a method for determining the set $Q_D$. Our method is strongly related to the theory of integral points on elliptic curves. The well-known Mordell's equation plays an important role as well in our considerations. Finally, some new conjectures will be included inspired by extensive calculation on a computer.
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Mathematica Slovaca. 2022, vol. 72, issue 1, p. 35-50.
https://www.degruyter.com/document/doi/10.1515/ms-2022-0003/html
https://www.degruyter.com/document/doi/10.1515/ms-2022-0003/html
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Peer-reviewed
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en