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WANG Yong-liang. Solutions to some Diophantine equations over mathbf{Q}(\sqrt{-3}[J]. Journal of East China Normal University (Natural Sciences), 2009, (5): 138-141.
Citation:
WANG Yong-liang. Solutions to some Diophantine equations over mathbf{Q}(\sqrt{-3}[J]. Journal of East China Normal University (Natural Sciences), 2009, (5): 138-141.
WANG Yong-liang. Solutions to some Diophantine equations over mathbf{Q}(\sqrt{-3}[J]. Journal of East China Normal University (Natural Sciences), 2009, (5): 138-141.
Citation:
WANG Yong-liang. Solutions to some Diophantine equations over mathbf{Q}(\sqrt{-3}[J]. Journal of East China Normal University (Natural Sciences), 2009, (5): 138-141.
By using Fermat’s method of descent, this paper proved that Diophantine equations { x^{4}-y^{4}=z^{2}} and { x^{4}+4y^{4}=z^{2}} have no non-trivial solutions over {\mathbf{Q}}(\sqrt{-3}), which implies that the Fermat Equation also has no non-trivial solutions in this field for n =4.