ARTICLE

doi:10.20944/preprints202307.2063.v9
Subject:
Computer Science And Mathematics,
Logic
Keywords:
constructive algorithms; constructive mathematics; current knowledge in a scientific discipline; current mathematical knowledge; informal mathematics; known algorithms
Online: 6 December 2023 (12:11:37 CET)
ARTICLE

doi:10.20944/preprints202303.0420.v7
Subject:
Computer Science And Mathematics,
Algebra And Number Theory
Keywords:
Brocard's problem; BrocardRamanujan equation x!+1=y^2; composite Fermat numbers; composite numbers of the form 2^(2^n)+1; Erd\"os' equation x(x+1)=y!
Online: 18 May 2023 (08:25:27 CEST)
ARTICLE
Subject:
Computer Science And Mathematics,
Logic
Keywords:
Alexander Zenkin's superinduction method; arithmetical operations on huge integers cannot be performed by any physical process; computable set {${\mathcal X} \subseteq N$} whose finiteness remains conjectured; computable set {${\mathcal X} \subseteq N$} whose infiniteness remains conjectured
Online: 25 February 2020 (10:06:45 CET)
ARTICLE

doi:10.20944/preprints201902.0156.v4
Subject:
Computer Science And Mathematics,
Logic
Keywords:
DavisPutnamRobinsonMatiyasevich theorem, Diophantine equation which has at most finitely many solutions in \mbox{nonnegative} integers, Hilbert's Tenth Problem, Hilbert's Tenth Problem for Q, Matiyasevich's theorem, recursively enumerable set, Smorynski's theorem
Online: 1 March 2019 (12:58:53 CET)
ARTICLE

doi:10.20944/preprints201804.0121.v2
Subject:
Computer Science And Mathematics,
Algebra And Number Theory
Keywords:
computable upper bound on the heights of rational solutions; computable upper bound on the moduli of integer solutions; Diophantine equation with a finite number of solutions; finitefold Diophantine representation; single query to an oracle that decides whether or not a given Diophantine equation has an integer solution; single query to an oracle that decides whether or not a given Diophantine equation has a rational solution
Online: 16 April 2018 (05:12:59 CEST)
ARTICLE

doi:10.20944/preprints201709.0127.v2
Subject:
Computer Science And Mathematics,
Logic
Keywords:
DavisPutnan RobinsonMatiyasevich theorem; Diophantine equation which has at most finitely many solutions in nonnegative integers; Diophantine equation which has at most finitely many solutions in positive integers; Diophantine equation which has at most finitely many integer solutions; Hilbert’s Tenth Problem; Matiyasevich’s theorem; recursively enumerable set; Smoryński’s theorem
Online: 27 September 2017 (04:05:45 CEST)