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On the continued fractions of quadratic and cubic irrationals

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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.

Literatur

  1. (1)

    « Journal f. d. r. u. ang. Mathematik »,175 (1936).

  2. (2)

    « Akad. v. Wetensch. te Amsterdam », Proc.39, 633–640, 729–737 (1936).

  3. (3)

    « Acta Mathematica »,79, 225–240 (1947). See alsoA. O. Gelfond, « Vestnik MGU »,9, 3 (1948) andTh. Schneider, « Math. Nachr. »,2, 288–295 (1949).

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Mahler, K. On the continued fractions of quadratic and cubic irrationals. Annali di Matematica 30, 147–172 (1949). https://doi.org/10.1007/BF02415005

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Keywords

  • Prime Factor
  • Continue Fraction
  • Regular Continue Fraction
  • Great Prime Factor