부산대학교 도서관

Summary: ``Mersenne primes $M_p$ are prime numbers of the form $2^p - 1$. The decimal expansion of $1/M_p$ is purely recurring, with period length $L$ that divides $M_p - 1$. If $p$ divides $L$, we partition the periodic part into $p$ blocks, each of length $\ell$. We show that there exists a permutation $B'_1, \dots , B'_p$ of the blocks such that (i) $B'_1 = 2B'_p - 10^\ell$, $B'_{k+1} = 2B'_k$ for $1 \leq k \leq p - 2$, $B'_p = 2B'_{p-1} + 1$, and (ii) $B'_1 + \cdots + B'_p = 10^\ell - 1$.''