Periodicity of Minimal Continued Fraction

Periodicity of Minimal Continued Fraction

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摘要 The minimal continued fraction of m (where 0<m∈Z is not a square) is connected with the corresponding simple continued fraction, from which it can be written out.In this paper, it is shown that the minimal continued fraction is periodic, its period is shorter than twice of the period of the corresponding simple continued fraction, its absolute\|period is not greater than the period of the corresponding simple continued fraction.Several properties of the minimal continued fraction are also obtained. The minimal continued fraction of m (where 0<m∈Z is not a square) is connected with the corresponding simple continued fraction, from which it can be written out.In this paper, it is shown that the minimal continued fraction is periodic, its period is shorter than twice of the period of the corresponding simple continued fraction, its absolute\|period is not greater than the period of the corresponding simple continued fraction.Several properties of the minimal continued fraction are also obtained.

作者林小雁

出处《Tsinghua Science and Technology》 SCIE EI CAS 1998年第4期1240-1242,共3页 清华大学学报（自然科学版（英文版）

基金 Supported by the Science Foundation of Tsinghua Uni-versity

关键词 semi\|simple continued fraction minimal continued fraction skipped point absolute\|period semi\|simple continued fraction minimal continued fraction skipped point absolute\|period

分类号 O156 [理学—基础数学]

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Tsinghua Science and Technology

1998年第4期

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Periodicity of Minimal Continued Fraction

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