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

2023/03/03 by Cantone, Domenico, Cuzziol, Luca, Omodeo, Eugenio G.
#03D25 #11D25 #FOS: Mathematics #Logic (math.LO) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2303.02208

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.

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