Abstract
We consider the Diophantine equation
where \({x \in \mathbb{Z}}\) and \({y \in \mathbb{Q}}\) are unknowns, f(x) and g(x) are non-zero integer polynomials in variable x and p is prime. We give bounds for x, when \({(x, y) \in \mathbb{Z} \times \mathbb{Q}}\) is a solution of the equation. This improves the results of some recent papers.
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Subburam, S., Togbé, A. On the Diophantine equation \({y^{p} = \frac{f(x)}{g(x)}}\). Acta Math. Hungar. 157, 1–9 (2019). https://doi.org/10.1007/s10474-018-0900-1
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DOI: https://doi.org/10.1007/s10474-018-0900-1