Mathematical Problem Idea

Hi all,

I think I have figured out what I will do for the mathematical problem I need to solve on this slog.

My idea is: to prove that a number is a multiple of 11 if starting from the right you take the first digit, then subtract the second digit, then add the third digit, then subtract the next and so forth; then if that number is a multiple of 11 (positive, negative or zero) then the original number is also a multiple of 11.

I think this might be able to be proved using complete induction. I see a few problems arising. One is proving that the number I get in the add subtract step is smaller than the previous number always (although I think I sorta see how to prove that). Another is how to prove that if the new number is a multiple of 11 the previous one is also. After that it could be fairly straight forward. I guess part of it will be seeing it in action with numbers where the add subtract step gets a number >= 11.

By the way I got this algorithm from http://www.counton.org/explorer/primes/divisibility-tests-for-9-and-11/

So long for now.