Summary
Let ξ be a quadratic or cubic irrational, and letp n /q n be then-th approximation of its regular continued fraction. It ist proved that the greatest prime factor ofq n tends to infinity withn.
Article PDF
Similar content being viewed by others
Literatur
« Journal f. d. r. u. ang. Mathematik »,175 (1936).
« Akad. v. Wetensch. te Amsterdam », Proc.39, 633–640, 729–737 (1936).
« Acta Mathematica »,79, 225–240 (1947). See alsoA. O. Gelfond, « Vestnik MGU »,9, 3 (1948) andTh. Schneider, « Math. Nachr. »,2, 288–295 (1949).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Mahler, K. On the continued fractions of quadratic and cubic irrationals. Annali di Matematica 30, 147–172 (1949). https://doi.org/10.1007/BF02415005
Issue Date:
DOI: https://doi.org/10.1007/BF02415005