Here is a test to determine whether a number is divisible by 19:

Remove the last digit of the number, add twice that digit to the truncated
number, and keep repeating this procedure until a number less than 20 is
obtained. The original number is divisible by 19 if and only if the final
number is 19. For example, the calculation below and to the left shows
that 25549 is __not__ divisible by 19, while the one on the right shows
that 47063 is divisible by 19.

- Find a similar test for divisibility by 29.
- Why does this work?

**Source: USA Mathematical Talent Search**

- What about a test for divisibility by 21?