Erman Isik
Published 2023-11-17Version 1
Recent results of Freitas, Kraus, Sengun and Siksek give sufficient criteria for the asymptotic Fermat's Last Theorem to hold over various number fields. In this paper, we prove asymptotic results about the solutions of the Diophantine equation $x^4-y^4=nz^p$ over various number fields using the modular method. For instance, we prove that the asymptotic generalised Fermat Theorem for the equation $x^4-y^4=2^\alpha z^p$ holds for infinitely many quadratic number fields.
Comments: arXiv admin note: text overlap with arXiv:2201.13270
About the Diophantine Equation $x^{4}-q^{4}=py^{r}$
Diophantine equations with Euler polynomials
Note on the diophantine equation X^t+Y^t=BZ^t
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