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Date: 5-12-2020
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Date: 31-10-2019
650
Date: 23-8-2020
1083
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The number of bases in which is a repeating decimal (actually, repeating -ary) of length is the same as the number of fractions , , ..., which have reduced denominator . For example, in bases 2, 3, ..., 6, 1/7 is given by
(1) |
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(2) |
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(3) |
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(4) |
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(5) |
which have periods 3, 6, 3, 6, and 2, respectively, corresponding to the denominators 6, 3, 2, 3, and 6 of
(6) |
REFERENCES:
Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, pp. 167-168, 1996.
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