The authors prove degeneracy of solution sets for two classes of one-parameter families of unit equations and extend GCD estimates for exponential Diophantine equations using the Ru-Vojta theorem and a higher-dimensional generalization of Huang-Levin-Xiao inequalities.
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Families of Unit Equations and Exponential Diophantine Problems via Integral Points
The authors prove degeneracy of solution sets for two classes of one-parameter families of unit equations and extend GCD estimates for exponential Diophantine equations using the Ru-Vojta theorem and a higher-dimensional generalization of Huang-Levin-Xiao inequalities.