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The Diophantine equations \(y^ 2 = x^ 4\pm 1\) in quadratic fields. (English) Zbl 0167.04005
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
MSC:
11D25 Cubic and quartic Diophantine equations
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