Diophantine problems related to cyclic cubic and quartic fields

DOI10.1016/J.JNT.2022.01.003zbMATH Open1508.11105arXiv2106.14558WikidataQ114156598 ScholiaQ114156598MaRDI QIDQ6371400

Szabolcs Tengely, Maciej Ulas

Publication date: 28 June 2021

Abstract: We are interested in solving the congruences $f^3+g^3+1equiv0pmodfg$ and $f^4-4g^2+4equiv0pmodfg$ in polynomials $f,g$ with rational coefficients. Moreover, we present results of computations of all integer points on certain one parametric curves of genus 1 and 3, related to cubic and quartic fields, respectively.

Mathematics Subject Classification ID

Units and factorization (11R27) Cubic and quartic extensions (11R16) Class numbers, class groups, discriminants (11R29) Cubic and quartic Diophantine equations (11D25)

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