English

On $k$-th power Diophantine triples of the form $\{a^k, b, c\}$

Number Theory 2026-04-28 v1

Abstract

In this paper, we prove that there are no kk-th power Diophantine triples of the form {ak,b,c}\{a^k,b,c\} for k3k\geq 3 and 1<ak<b<c1<a^k<b<c.

Keywords

Cite

@article{arxiv.2604.24650,
  title  = {On $k$-th power Diophantine triples of the form $\{a^k, b, c\}$},
  author = {Clemens Fuchs and Miriam Schönauer},
  journal= {arXiv preprint arXiv:2604.24650},
  year   = {2026}
}