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## 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[itex]\equiv[/itex]0 mod 3

n=X1* 10^n+ x2*10^n-1......Xn

so need to prove(x1+x2+......Xn)[itex]\equiv[/itex]0 mod 3, the how to prove the next step