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A Hasse-type principle for exponential Diophantine equations and its applications


Authors: Csanád Bertók and Lajos Hajdu
Journal: Math. Comp. 85 (2016), 849-860
MSC (2010): Primary 11D61, 11D72, 11D79
DOI: https://doi.org/10.1090/mcom/3002
Published electronically: July 16, 2015
MathSciNet review: 3434884
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Abstract: We propose a conjecture, similar to Skolem's conjecture, on a Hasse-type principle for exponential Diophantine equations. We prove that in a sense the principle is valid for ``almost all'' equations. Based upon this we propose a general method for the solution of exponential Diophantine equations. Using a generalization of a result of Erdős, Pomerance and Schmutz concerning Carmichael's $ \lambda $ function, we can make our search systematic for certain moduli needed in the method.


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Additional Information

Csanád Bertók
Affiliation: Institute of Mathematics, University of Debrecen, H-4010 Debrecen, P.O. Box 12, Hungary
Email: bertok.csanad@science.unideb.hu

Lajos Hajdu
Affiliation: Institute of Mathematics, University of Debrecen, H-4010 Debrecen, P.O. Box 12, Hungary
Email: hajdul@science.unideb.hu

DOI: https://doi.org/10.1090/mcom/3002
Keywords: Exponential Diophantine equations, Hasse-principle, Carmichael's function
Received by editor(s): July 24, 2014
Received by editor(s) in revised form: August 25, 2014, October 1, 2014, and October 10, 2014
Published electronically: July 16, 2015
Additional Notes: This research was supported in part by the OTKA grants K100339 and NK101680, and by the TÁMOP-4.2.2.C-11/1/KONV-2012-0001 project. The project was supported by the European Union, co-financed by the European Social Fund.
Article copyright: © Copyright 2015 American Mathematical Society

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