LAGRANGE’S THEOREM AND 2- CONTINUED FRACTION EXPANSION

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Date

2019

Journal Title

Journal ISSN

Volume Title

Publisher

СДУ хабаршысы - 2019

Abstract

Abstract. The simple continued fraction theory is a sub-branch of number theory that is well developed. One of the classical results is due to Lagrange which states that the simple continued fraction expansion of a real number has eventually periodic expansion if and only if it is quadratic irrational. Similar results are not available when one considers N-continued fraction expansion which is not so well developed theory. In this article, authors aim to provide computational evidence when a quadratic irrational may not necessarily have eventually periodic 2-continued fraction expansion. Moreover, a proof is provided for a special type of real numbers for which Lagrange’s theorem does hold.

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Keywords

Lagrange’s theorem, N-continued fraction, Mathematica software, quadratic irrational number, СДУ хабаршысы - 2019, №1

Citation

Sh. Kadyrov , F. Mashurov / LAGRANGE’S THEOREM AND 2- CONTINUED FRACTION EXPANSION / СДУ хабаршысы - 2019