Euler,s Totient Rule
المؤلف:
Conway, J. H. and Guy, R. K
المصدر:
The Book of Numbers. New York: Springer-Verlag
الجزء والصفحة:
pp. 167-168
24-11-2019
913
Euler's Totient Rule
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
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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