Halfway to a solution of X 2 -DY 2 =-3
Journal de Théorie des Nombres de Bordeaux, Tome 6 (1994) no. 2, pp. 421-457.

Il est bien connu que le développement en fraction continue de D donne facilement le milieu du cycle principal des idéaux, c’est à dire le point à mi-parcourt d’une solution de x 2 -Dy 2 =±1. Nous montrons ici que de façon analogue le point à mi-parcourt d’une solution de x 2 -Dy 2 =-3 peut-être reconnu. Nous expliquons ce qu’il en est.

It is well known that the continued fraction expansion of D readily displays the midpoint of the principal cycle of ideals, that is, the point halfway to a solution of x 2 -Dy 2 =±1. Here we notice that, analogously, the point halfway to a solution of x 2 -Dy 2 =-3 can be recognised. We explain what is going on.

DOI : https://doi.org/10.5802/jtnb.123
Classification : 11A55
Mots clés : continued fraction, ideal, quadratic form, ambiguous cycle
@article{JTNB_1994__6_2_421_0,
     author = {Mollin, Richard A. and van der Poorten, Alferd J. and Williams, H. C.},
     title = {Halfway to a solution of $X^2 - DY^2 = -3$},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {421--457},
     publisher = {Universit\'e Bordeaux I},
     volume = {6},
     number = {2},
     year = {1994},
     doi = {10.5802/jtnb.123},
     zbl = {0820.11015},
     mrnumber = {1360654},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.123/}
}
R. A. Mollin; A. J. Van der Poorten; H. C. Williams. Halfway to a solution of $X^2 - DY^2 = -3$. Journal de Théorie des Nombres de Bordeaux, Tome 6 (1994) no. 2, pp. 421-457. doi : 10.5802/jtnb.123. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.123/

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