On the period length of some special continued fractions
R. A. Mollin ; H. C. Williams
Journal de Théorie des Nombres de Bordeaux, Tome 4 (1992) no. 1, pp. 19-42.

We investigate and refine a device which we introduced in [3] for the study of continued fractions. This allows us to more easily compute the period lengths of certain continued fractions and it can be used to suggest some aspects of the cycle structure (see [1]) within the period of certain continued fractions related to underlying real quadratic fields.

@article{JTNB_1992__4_1_19_0,
     author = {Mollin, Richard A. and Williams, H. C.},
     title = {On the period length of some special continued fractions},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {19--42},
     publisher = {Universit\'e Bordeaux I},
     volume = {4},
     number = {1},
     year = {1992},
     doi = {10.5802/jtnb.62},
     zbl = {0766.11003},
     mrnumber = {1183916},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.62/}
}
R. A. Mollin; H. C. Williams. On the period length of some special continued fractions. Journal de Théorie des Nombres de Bordeaux, Tome 4 (1992) no. 1, pp. 19-42. doi : 10.5802/jtnb.62. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.62/

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[2] D.E. Knuth, The Art of Computer Programing II: Seminumerical Algorithms, Addison-Wesley, 1981. | MR 633878

[3] R.A. Mollin and H.C. Williams, Consecutive powers in continued fractions, (to appear: Acta Arithmetica). | Zbl 0764.11010

[4] O. Perron, Die Lehre von den Kettenbrüchen, Chelsea, New-York (undated).

[5] J.W. Porter, On a theorem of Heilbronn, Mathematika 22 (1975), 20-28. | MR 498452 | Zbl 0316.10019