Proving: a ≡ s (mod 9) | Basic Proof for Congruence Modulo 9

[scottstapp]

Homework Statement

Prove the following
a is congruent to s(mod 9)

Homework Equations

a=d_rd_r-1***d₁d₀

a=d₀+ d₁10+ d₂10²+...+d_r10^r

s= d₀+ d₁ +...+d_r

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+...+d_r10^r which is congruent to d₀+ d₁+ d₂+...+d_r (mod 9).

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

 

[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.

 

[scottstapp]

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

 

[Dick]

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

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.