On Patterns Occurring in Binary Algebraic Numbers

@inproceedings{Adamczewski2007OnPO,
  title={On Patterns Occurring in Binary Algebraic Numbers},
  author={Boris Adamczewski},
  year={2007}
}
We prove that every algebraic number contains infinitely many occurrences of 7/3-powers in its binary expansion. Using the same approach, we also show that every algebraic number contains either infinitely many occurrences of squares or infinitely many occurrences of one of the blocks 010 or 02120 in its ternary expansion. 

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References

Publications referenced by this paper.
Showing 1-9 of 9 references

Sur les chiffres décimaux de √ 2 et divers problèmes de probabilités en châıne

  • É. Borel
  • C. R. Acad. Sci. Paris 230
  • 1950

Arithmetische Eigenschaften der Lösungen einer Klasse von Funktionalgleichungen

  • K. Mahler
  • Math. Annalen 101 (1929), 342–366. Corrigendum…
  • 1930

Über die gegenseitige Lage gleicher Teile gewisser Zeichenreihen

  • A. Thue
  • Norske vid. Selsk. Skr. Mat. Nat. Kl. 1
  • 1912

Sur la complexité des nombres algébriques

  • B. Adamczewski, Y. Bugeaud, F. Luca
  • C. R. Acad. Sci. Paris 339 (2004), 11–14…
  • 1033

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