English

Creating Decidable Diophantine Equations

Number Theory 2024-06-11 v3

Abstract

Generalizing an argument of Matiyasevich, we illustrate a method to generate infinitely many diophantine equations whose solutions can be completely described by linear recurrences. In particular, we provide an integer-coefficient polynomial p(x,y,z)p(x, y, z) whose only integer roots are consecutive triples of Tribonacci numbers.

Keywords

Cite

@article{arxiv.2404.01483,
  title  = {Creating Decidable Diophantine Equations},
  author = {Robert Dougherty-Bliss and Charles Kenney and Doron Zeilberger},
  journal= {arXiv preprint arXiv:2404.01483},
  year   = {2024}
}

Comments

This version corrects a misstated date

R2 v1 2026-06-28T15:40:50.427Z