Diophantine problems related to cyclic cubic and quartic fields
Abstract
We are interested in solving the congruences f3+g3+1 0fg and f4-4g2+4 0fg 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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