English

Six equations in search of a finite-fold-ness proof

Number Theory 2024-10-01 v3 Logic

Abstract

By following the same construction pattern which Martin Davis proposed in a 1968 paper of his, we have obtained six quaternary quartic Diophantine equations that candidate as `rule-them-all' equations: proving that one of them has only a finite number of integer solutions would suffice to ensure that each recursively enumerable set admits a finite-fold polynomial Diophantine representation.

Keywords

Cite

@article{arxiv.2303.02208,
  title  = {Six equations in search of a finite-fold-ness proof},
  author = {Domenico Cantone and Luca Cuzziol and Eugenio G. Omodeo},
  journal= {arXiv preprint arXiv:2303.02208},
  year   = {2024}
}