English

Frobenius numbers associated with Diophantine triples of $x^2+y^2=z^r$ (extended version)

Number Theory 2024-03-13 v1 Combinatorics

Abstract

We give an explicit formula for the pp-Frobenius number of triples associated with Diophantine equations x2+y2=zrx^2+y^2=z^r, that is, the largest positive integer that can only be represented in pp ways by combining the three integers of the solutions of Diophantine equations x2+y2=zrx^2+y^2=z^r. When r=2r=2, the Frobenius number has already been given.

Keywords

Cite

@article{arxiv.2403.07534,
  title  = {Frobenius numbers associated with Diophantine triples of $x^2+y^2=z^r$ (extended version)},
  author = {Takao Komatsu and Neha Gupta and Manoj Upreti},
  journal= {arXiv preprint arXiv:2403.07534},
  year   = {2024}
}