Geodesic
Pell Equations: Non-Principal Lagrange Criteria and Central Norms
Canadian mathematical bulletin, Tome 55 (2012) no. 4, pp. 774-782

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DOI

We provide a criterion for the central norm to be any value in the simple continued fraction expansion of $\sqrt{D}$ for any non-square integer $D\,>\,1$ . We also provide a simple criterion for the solvability of the Pell equation ${{x}^{2}}\,-\,D{{y}^{2}}\,=\,-1$ in terms of congruence conditions modulo $D$ .
DOI : 10.4153/CMB-2011-118-9
Mots-clés : 11D09, 11A55, 11R11, 11R29, Pell's equation, continued fractions, central norms 
Mollin, R. A.; Srinivasan, A. Pell Equations: Non-Principal Lagrange Criteria and Central Norms. Canadian mathematical bulletin, Tome 55 (2012) no. 4, pp. 774-782. doi: 10.4153/CMB-2011-118-9
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     author = {Mollin, R. A. and Srinivasan, A.},
     title = {Pell {Equations:} {Non-Principal} {Lagrange} {Criteria} and {Central} {Norms}},
     journal = {Canadian mathematical bulletin},
     pages = {774--782},
     year = {2012},
     volume = {55},
     number = {4},
     doi = {10.4153/CMB-2011-118-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-118-9/}
}
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