MathDB

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

N_k

with the following property: for all

n \ge N_k

, we can glue the numbers

1,2,\dots,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

Problem Statement