# Rule of 9 proof

1. Feb 18, 2010

### scottstapp

1. The problem statement, all variables and given/known data
Prove the following
a is congruent to s(mod 9)

2. Relevant equations
a=drdr-1***d1d0

a=d0+ d110+ d2102+...+dr10r

s= d0+ d1 +...+dr

3. The attempt at a solution

we know that 10-1=9 so we can say that 10 is congruent to 1(mod 9)

so we know that a is congruent to d0+ d110+ d2102+...+dr10r which is congruent to d0+ d1+ d2+...+dr (mod 9).

Is this a step in the right direction? Does anything else need to be shown?

2. Feb 18, 2010

### Dick

Not much else needs to be shown. You could fill in some details, like saying why 10^2, 10^3 etc are also congruent to 1 mod 9. But I'm guessing you've got the idea.

Last edited: Feb 18, 2010
3. Feb 18, 2010

### scottstapp

I guess what I was trying to ask was is the way I wrote a valid formal proof?

4. Feb 18, 2010

### Dick

You wrote a valid INFORMAL proof. I.e. one where you don't detail all of the reasons for every step. If you want a formal proof, you should supply those reasons.