Midy,s Theorem
المؤلف:
Rademacher, H. and Toeplitz, O
المصدر:
The Enjoyment of Mathematics: Selections from Mathematics for the Amateur. Princeton, NJ: Princeton University Press,
الجزء والصفحة:
...
27-10-2019
1156
Midy's Theorem
If the period of a repeating decimal for 
, where 
is prime and 
is a reduced fraction, has an even number of digits, then dividing the repeating portion into halves and adding gives a string of 9s. For example, 
, and 
.
REFERENCES:
Rademacher, H. and Toeplitz, O. The Enjoyment of Mathematics: Selections from Mathematics for the Amateur. Princeton, NJ: Princeton University Press, pp. 158-160, 1957.
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