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Undecidable and decidable restrictions of Hilbert's Tenth Problem: images of polynomials vs. images of exponential functions
Author(s) -
Prunescu Mihai
Publication year - 2006
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.200510013
Subject(s) - diophantine equation , undecidable problem , mathematics , decidability , exponential function , section (typography) , diophantine set , exponential polynomial , pure mathematics , discrete mathematics , mathematical analysis , computer science , operating system
Abstract Classical results of additive number theory lead to the undecidability of the existence of solutions for diophantine equations in given special sets of integers. Those sets which are images of polynomials are covered by a more general result in the second section. In contrast, restricting diophantine equations to images of exponential functions with natural bases leads to decidable problems, as proved in the third section. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)