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On two conjectures of P. Chowla and S. Chowla concerning continued fractions

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Summary

The alternating sum of the partial quotients in the primitive period of a continued fraction expansion of √D is determined mod 2 and mod 3.

References

  1. [1]

    P. Chowla -S. Chowla,Some properties of periodic simple continued fractions, Proc. Nat. Acad. Sci. USA,69 (1972), pp. 37–45.

  2. [2]

    H. Lang,Über die Klassenzahlen eines imaginären bizyklischen biquadratischen Zahlkörpers und seines reellquadratischen Teilkörpers, J. Reine angew. Math., 262/263 (to appear).

  3. [3]

    T. Nagell,Contribution to the theory of a category of diophantine equations of the second degree with two unknowns, Nova Acta Regiae Soc. Sc. Upsaliensis, (4),16 (1954), no. 2.

  4. [4]

    O. Perron,Die Lehre von den Kettenbrüchen, 2 te Auflage, reprinted by Chelsea (New York).

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Additional information

To Professor BeniaminoSegre on his 70-th birthday.

Pervenuto il 7 maggio 1973.

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Schinzel, A. On two conjectures of P. Chowla and S. Chowla concerning continued fractions. Annali di Matematica 98, 111–117 (1974). https://doi.org/10.1007/BF02414016

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Keywords

  • Continue Fraction Expansion
  • Partial Quotient
  • Primitive Period