Effective upper bounds for y^a in the equation y^a equals sum of convergent denominators to quadratic irrational alpha are obtained from Hamming weights in radix and Zeckendorf representations, extending Vukusic-Ziegler and yielding an analogue of Kebli-Kihel-Larone-Luca.
Class ical and modular approaches to exponential Diophantine equations
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Representing an integer and its powers in two unrelated number systems
Effective upper bounds for y^a in the equation y^a equals sum of convergent denominators to quadratic irrational alpha are obtained from Hamming weights in radix and Zeckendorf representations, extending Vukusic-Ziegler and yielding an analogue of Kebli-Kihel-Larone-Luca.