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}
}