Number theory problem divisible

[yeland404]

Homework Statement

Prove that n ℂ Z+ is divisible by 3( respectively 9). to show that if and only if the sum of its digits is divisible by 3

Homework Equations

The Attempt at a Solution

so n= 3q, q>3 that n\equiv0 mod 3
n=X1* 10^n+ x2*10^n-1...Xn
so need to prove(x1+x2+...Xn)\equiv0 mod 3, the how to prove the next step

 

[Dick]

Homework Statement

Prove that n ℂ Z+ is divisible by 3( respectively 9). to show that if and only if the sum of its digits is divisible by 3

Homework Equations

The Attempt at a Solution

so n= 3q, q>3 that n\equiv0 mod 3
n=X1* 10^n+ x2*10^n-1...Xn
so need to prove(x1+x2+...Xn)\equiv0 mod 3, the how to prove the next step

Show 10^k=1 mod 3.

 

[Deveno]

and for extra credit, google "casting out nines" for a better explanation of why this works (the same theorem holds for the number 9, in fact, for the same reason).