Diophantine problems related to cyclic cubic and quartic fields
نویسندگان
چکیده
We are interested in solving the congruences f3+g3+1≡0(modfg) and f4−4g2+4≡0(modfg) polynomials f,g with rational coefficients. Moreover, we present results of computations all integer points on certain one parametric curves genus 1 3, related to cubic quartic fields, respectively. Our approach is based Gröbner basis techniques do numerical experiences it. mainly deal case degf≤2 prove that there no new families cyclic nor fields. In fields obtained a polynomial was not discovered by Balady Washington [2], it given t4+7890798742t3−37333446t2+38618t+1.
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2022
ISSN: ['0022-314X', '1096-1658']
DOI: https://doi.org/10.1016/j.jnt.2022.01.003