Szabolcs Tengely, Maciej Ulas
Published 2021-06-28Version 1
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.
Integer points on homogeneous varieties with two or more degrees
Laurent series expansions of multiple zeta-functions of Euler-Zagier type at integer points
Rational approximation to surfaces defined by polynomials in one variable
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