Abstract
Abstract
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
$\mathbb{Q}(i)$
.
Publisher
Cambridge University Press (CUP)
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