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Recent results of Freitas, Kraus, Sengun and Siksek give sufficient criteriafor the asymptotic Fermat's Last Theorem to hold over various number fields. Inthis paper, we prove asymptotic results about the solutions of the Diophantineequation $x^4-y^4=nz^p$ over various number fields using the modular method.For instance, we prove that the asymptotic generalised Fermat Theorem for theequation $x^4-y^4=2^\alpha z^p$ holds for infinitely many quadratic numberfields.

On Modular Approach to Diophantine Equation $x^4-y^4=nz^p$ over Number Fields