Lagrange, central norms, and quadratic Diophantine equations
2005 ◽
Vol 2005
(7)
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pp. 1039-1047
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Keyword(s):
We consider the Diophantine equation of the formx2−Dy2=c, wherec=±1,±2, and provide a generalization of results of Lagrange with elementary proofs using only basic properties of simple continued fractions. As a consequence, we achieve a completely general, simple, and elegant criterion for the central norm to be2in the simple continued fraction expansion ofD.
2009 ◽
Vol 29
(5)
◽
pp. 1451-1478
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2018 ◽
Vol 2019
(19)
◽
pp. 6136-6161
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1991 ◽
Vol 51
(2)
◽
pp. 324-330
◽
2001 ◽
Vol 64
(2)
◽
pp. 331-343
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