Midy's Theorem

If the period of a repeating decimal for a/p, where p is prime and a/p 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, 1/7=0.142857^_, and 142+857=999.

See also

Decimal Expansion, Repeating Decimal

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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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Midy's Theorem

Cite this as:

Weisstein, Eric W. "Midy's Theorem." From MathWorld--A Wolfram Web Resource.

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