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

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- by Csanád Bertók and Lajos Hajdu PDF
- Math. Comp.
**85**(2016), 849-860 Request permission

## 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.## References

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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
- MR Author ID: 339279
- Email: hajdul@science.unideb.hu
- 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.
- © Copyright 2015 American Mathematical Society
- Journal: Math. Comp.
**85**(2016), 849-860 - MSC (2010): Primary 11D61, 11D72, 11D79
- DOI: https://doi.org/10.1090/mcom/3002
- MathSciNet review: 3434884