Abstract
Let A, B, C be some nonconstant polynomials with coefficients in a field K of characteristic zero. We prove that the polynomial Pillai equation \(A^x-B^y=C\) has at most one solution in positive integers x, y except for three explicitly described triplets \((A,B,C) \in K[t]^3\) when it has exactly two solutions in \((x,y) \in \mathbb {N}^2\).
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Acknowledgements
I thank the referee for some corrections. This research was funded by the European Social Fund according to the activity ‘Improvement of researchers’ qualification by implementing world-class R&D projects’ of Measure No. 09.3.3-LMT-K-712-01-0037.
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Dubickas, A. Pillai’s Equation in Polynomials. Mediterr. J. Math. 18, 63 (2021). https://doi.org/10.1007/s00009-021-01706-8
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DOI: https://doi.org/10.1007/s00009-021-01706-8