Geodesic
Unisequences and nearest integer continued fraction midpoint criteria for Pell's equation
Journal of integer sequences, Tome 12 (2009) no. 6.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: The nearest integer continued fractions of Hurwitz, Minnegerode (NICF-H) and in Perron's book Die Lehre von den Kettenbrüchen (NICF-P) are closely related. Midpoint criteria for solving Pell's equation $x^{2} - Dy^{2} = \pm 1$ in terms of the NICF-H expansion of $\sqrt D$ were derived by H. C. Williams using singular continued fractions. We derive these criteria without the use of singular continued fractions. We use an algorithm for converting the regular continued fraction expansion of $\sqrt D$ to its NICF-P expansion.
Classification : 11A55, 11Y65
Keywords: nearest integer continued fraction, period-length, midpoint criteria, unisequence 
@article{JIS_2009__12_6_a7,
     author = {Matthews, Keith R.},
     title = {Unisequences and nearest integer continued fraction midpoint criteria for {Pell's} equation},
     journal = {Journal of integer sequences},
     publisher = {mathdoc},
     volume = {12},
     number = {6},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2009__12_6_a7/}
}
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Matthews, Keith R. Unisequences and nearest integer continued fraction midpoint criteria for Pell's equation. Journal of integer sequences, Tome 12 (2009) no. 6. http://geodesic.mathdoc.fr/item/JIS_2009__12_6_a7/