MathDB

A change in a natural number

n

consists of adding a pair of zeros between two digits or at the end of the decimal representation of

n

. A countryman of

n

is a number that can be obtained from one or more changes in

n

. For example.

40041

4410000

and

4004001

are all countrymen from

441

. Determine all the natural numbers

n

for which there is a natural number m with the property that

n

divides

m

and all the countrymen of

m

Problem Statement