Distribution of digits in periodic decimals

Joseph Lewittes

Abstract: Consider fractions $\frac{a}{N}$, $0<a<N$, and their periodic expansions in base $B$, $(B,N)=1$. Our interest is in the number of times a $B$-digit $b$ occurs among the periods of all such fractions, for fixed $N$, and also in the number of occurances of $b$ among the proper periods, those where $(a,N)=1$. Some historical perspective on this problem is also included.

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