Kadyrov Sh.Mashurov F.2023-11-162023-11-162019Sh. Kadyrov , F. Mashurov / LAGRANGE’S THEOREM AND 2- CONTINUED FRACTION EXPANSION / СДУ хабаршысы - 20192415-8135https://repository.sdu.edu.kz/handle/123456789/794Abstract. 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.enLagrange’s theoremN-continued fractionMathematica softwarequadratic irrational numberСДУ хабаршысы - 2019№1Article