MathDB

Given a positive integer

N

(written in base

10

), define its integer substrings to be integers that are equal to strings of one or more consecutive digits from

N

, including

N

itself. For example, the integer substrings of

3208

are

3

2

0

8

32

20

320

208

3208

. (The substring

08

is omitted from this list because it is the same integer as the substring

8

, which is already listed.)
What is the greatest integer

N

such that no integer substring of

N

is a multiple of

9

? (Note:

0

is a multiple of

9

Problem Statement