A String Of Ones

.
.

. .
.
.

Subj:     MATH PROB. - A String Of Ones (S503)
          From: MathsChallenge.net on 9/13/2006
Source: http://mathschallenge.net/index.php?section=
         problems&show=true&titleid=string_of_ones

A number consisting entirely of the digit one is called
a repunit; for example, 11111.

Find the smallest repunit that is divisible by 63.

The following solution was sent in by Abe:

A string of 18 1's. Using divisibility rules for 7 and 9 from http://mathforum.org/k12/mathtips/ward2.html.