Some periodic continued fractions with long periods
Authors:
C. D. Patterson and H. C. Williams
Journal:
Math. Comp. 44 (1985), 523532
MSC:
Primary 11Y65; Secondary 11A55, 11J70
MathSciNet review:
777283
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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 DLS127, 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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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198507772831
PII:
S 00255718(1985)07772831
Article copyright:
© Copyright 1985
American Mathematical Society
