MathDB

We say a positive integer

n

k

-special if none of its figures is zero and, for any permutation the figures of

n

, the resulting number is multiple of

k

. Let

m\ge 2

be a positive integer.
[*] Find the number of

4

-special numbers with

m

figures. [*] Find the number of

3

-special numbers with

m

figures.

Problem Statement