Glasnik Matematicki, Vol. 46, No. 2 (2011), 269-282.

PERIOD-LENGTH EQUALITY FOR THE NEAREST INTEGER AND NEAREST SQUARE CONTINUED FRACTION EXPANSIONS OF A QUADRATIC SURD

Keith R. Matthews and John P. Robertson

Department of Mathematics, University of Queensland, Brisbane, Australia, 4072
and
Centre for Mathematics and its Applications, Australian National University, Canberra, ACT, Australia, 0200
e-mail: keithmatt@gmail.com

Actuarial and Economic Services Division, National Council on Compensation Insurance, Boca Raton, 33487, USA
e-mail: jpr2718@gmail.com


Abstract.   We prove equality of the period-lengths of the nearest integer continued fraction and the nearest square continued fraction, for arbitrary real quadratic irrationals.

2000 Mathematics Subject Classification.   11A55, 11Y65.

Key words and phrases.   Nearest square continued fraction, nearest integer continued fraction, period-length, reduced quadratic irrational.


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DOI: 10.3336/gm.46.2.01


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