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Published online by Cambridge University Press: 10 November 2023
We investigate the equation $D=x^4-y^4$ in field extensions. As an application, for a prime number p, we find solutions to
$p=x^4-y^4$ if
$p\equiv 11$ (mod 16) and
$p^3=x^4-y^4$ if
$p\equiv 3$ (mod 16) in all cubic extensions of
$\mathbb{Q}(i)$.