English

Diophantine equations in separated variables and polynomial power sums

Number Theory 2023-04-12 v1

Abstract

We consider Diophantine equations of the shape f(x)=g(y) f(x) = g(y) , where the polynomials f f and g g are elements of power sums. Using a finiteness criterion of Bilu and Tichy, we will prove that under suitable assumptions infinitely many rational solutions (x,y) (x,y) with a bounded denominator are only possible in trivial cases.

Keywords

Cite

@article{arxiv.2008.10342,
  title  = {Diophantine equations in separated variables and polynomial power sums},
  author = {Clemens Fuchs and Sebastian Heintze},
  journal= {arXiv preprint arXiv:2008.10342},
  year   = {2023}
}

Comments

6 pages

R2 v1 2026-06-23T18:03:36.065Z