Define glueing of positive integers as writing their base ten representations one after another and
interpreting the result as the base ten representation of a single positive integer.
Find all positive integers k for which there exists an integer Nk with the following property: for all n≥Nk, we can glue the numbers 1,2,…,n in some order so that the result is a number divisible by k.
Remark. The base ten representation of a positive integer never starts with zero.
Example. Glueing 15,14,7 in this order makes 15147. number theorynumber theory proposedDigits