A Little Mathematical Proof

2009-11-06

Did you know that if you take any non-negative integer, then subtract the sum of its digits, the answer will always be divisible by 9?

For example, today's date is 11/06. 1106-(1+1+6) = 1098, and 1098/9 = 122.

Curious why? Here's a more general proof [pdf], that the difference between a number and the sum of its digits (if written in base b) will always be divisible by (b-1).