Some periodic continued fractions with long periods

Authors:
C. D. Patterson and H. C. Williams

Journal:
Math. Comp. **44** (1985), 523-532

MSC:
Primary 11Y65; Secondary 11A55, 11J70

DOI:
https://doi.org/10.1090/S0025-5718-1985-0777283-1

MathSciNet review:
777283

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be the period length of the continued fraction for . Under the extended Riemann Hypothesis for one would expect that . In order to test this it is necessary to find values of *D* for which is large. This, in turn, requires that we be able to find solutions to large sets of simultaneous linear congruences. The University of Manitoba Sieve Unit (UMSU), a machine similar to D. H. Lehmer's DLS-127, was used to find such values of *D*. For example, if , then 25679652. Some results are also obtained for the Voronoi continued fraction for .

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DOI:
https://doi.org/10.1090/S0025-5718-1985-0777283-1

Article copyright:
© Copyright 1985
American Mathematical Society