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On a theorem of Heilbronn

Published online by Cambridge University Press:  26 February 2010

J. W. Porter
J. W. Porter
Affiliation:
Department of Pure Mathematics, University College, Cardiff.
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Extract

In an article [2] in a volume of papers dedicated to the memory of Edmund Landau, Heilbronn investigates the following problem on continued fractions, posed by Dr. J. Gillis:

Let a and N be natural numbers such that 1 ≤ a < N and (a, N) = 1. Then there exist unique natural numbers ci such that

Type
Research Article
Information
Mathematika , Volume 22 , Issue 1 , June 1975 , pp. 20 - 28
Copyright
Copyright © University College London 1975

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References

1. Estermann, T.. “Über die Darstellung einer Zahl als Differenz von zwei Produkten”, J. für Math., 1964 (1931), 173–82.Google Scholar
2. Heilbronn, H.. “On the average length of a class of finite continued fractions”, Abhandlungen aus Zahlentheorie und Analysis zur Erinnerung an Edmund Landau (Berlin and New York), 87–96.Google Scholar
3. Tonkov, T.. “On the average length of finite continued fractions”, Ada Arith., 26 (1974), 47–57.CrossRefGoogle Scholar
4. Weil, A.. “On some exponential sums”, Proc. Nat. Acad. Sci. U.S.A., 34 (1934), 204–207.CrossRefGoogle Scholar