Mordell, L. J. The Diophantine equations \(y^ 2 = x^ 4\pm 1\) in quadratic fields. (English) Zbl 0167.04005 J. Lond. Math. Soc. 44, 112-114 (1969). The author investigates non-trivial solutions of \(y^2=x^4\pm 1\) in a quadratic field \(\mathbb Q(\sqrt d)\), \(d\) rational. With the \(+\) sign in the equation, he shows that such solutions exist only if \(d=b^4\pm 12b^2+4\), \(b\) rational. Similarly, with the \(-\) sign, \(d\) must be \(b^4-12b^2+32b-28\), \(b\) again rational. Reviewer: G. L. Watson Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page MSC: 11D25 Cubic and quartic Diophantine equations Keywords:quartic Diophantine equations; quadratic fields PDF BibTeX XML Cite \textit{L. J. Mordell}, J. Lond. Math. Soc. 44, 112--114 (1969; Zbl 0167.04005) Full Text: DOI