On the Diophantine equation y p = f ( x ) g ( x )

On the Diophantine equation y p = f ( x ) g ( x )

We consider the Diophantine equationyp=f(x)g(x),where x∈Z and y∈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)∈Z×Q is a solution of the equation. This improves the results of some recent papers.

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Veröffentlicht in:Acta mathematica Hungarica 2019-01, Vol.157 (1), p.1-9
Hauptverfasser: Subburam, S, Togbé, A
Format: Artikel
Sprache:eng
Schlagworte:
Diophantine equation
Mathematics
Polynomials
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Zusammenfassung:We consider the Diophantine equationyp=f(x)g(x),where x∈Z and y∈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)∈Z×Q is a solution of the equation. This improves the results of some recent papers.
ISSN:0236-5294
1588-2632
DOI:10.1007/s10474-018-0900-1