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arXiv · 2106.14558

Diophantine problems related to cyclic cubic and quartic fields

Szabolcs Tengely·Maciej Ulas
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Abstract

We are interested in solving the congruences $f^3+g^3+1\equiv 0\pmod{fg}$ and $f^4-4g^2+4\equiv 0\pmod{fg}$ 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.

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Szabolcs Tengely, Maciej Ulas. 2021-06-28. Diophantine problems related to cyclic cubic and quartic fields. https://arxiv.org/abs/2106.14558

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