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

2014/07/24 by Bertok, Cs., Hajdu, L. · 1 citation
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1407.6499

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 λ function, we can make our search systematic for certain moduli needed in the method.

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