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# polydivisible number

Given a base $b$ integer $n$ with $k$ digits $d_{1},\ldots,d_{k}$, consider $d_{k}$ the least significant digit and $d_{1}$, to suit our purpose in this case. If for each $1<j<k$ it is the case that

$(\sum_{{i=1}}^{j}d_{i}b^{{k-j-i}})|j,$ |

then $n$ is said to be a polydivisible number.

A reasonably good estimate of how many polydivisible numbers base $b$ has is

$\sum_{{i=2}}^{{b-1}}\frac{(b-1)b^{{i-1}}}{i!}.$ |

In any given base, there is only one polydivisible number that is also a pandigital number.

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## Mathematics Subject Classification

11A63*no label found*

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