Browsing by Author "Mashurov F."

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