Practical solution of some families of quartic and sextic diophantine hyperelliptic equations

Konstantinos A. Draziotis

Practical solution of some families of quartic and sextic diophantine hyperelliptic equations

Number Theory 2022-11-17 v3

Authors: Konstantinos A. Draziotis

Abstract

Using elementary number theory we study Diophantine equations over the rational integers of the following form, $y^2=(x+a)(x+a+k)(x+b)(x+b+k)$ , $y^2=c^2x^4+ax^2+b$ and $y^2=(x^2-1)(x^2-\alpha^2)(x^2-(\alpha+1)^2).$ We express their integer solutions by means of the divisors of the discriminant of $f(x),$ where $y^2=f(x)$ .

Keywords

diophantine equations hyperelliptic curves quartic equations sextic equations elementary number theory integer solutions discriminant

Cite

@article{arxiv.2207.10754,
  title  = {Practical solution of some families of quartic and sextic diophantine hyperelliptic equations},
  author = {Konstantinos A. Draziotis},
  journal= {arXiv preprint arXiv:2207.10754},
  year   = {2022}
}

Comments

Corrected typos; rewrite abstract; Revised a corollary 2.5, result changed;minor change to title

Practical solution of some families of quartic and sextic diophantine hyperelliptic equations

Abstract

Keywords

Cite

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