Math PROOF for divisibility of 3 rule
I have to write a math proof for the following rule:
A number is divisible by 3 if and only if the sum of its digits are divisible by 3.
My teacher gave us an example of a mathematical proof of the divisibility rule for 9 which is the same as 3 - A number is divisible by 9 if and only if the sum of its digits are divisible by 9
t+u=9
u=9-t
N=10t+u
N=10t+9-t
N=9t+9
N=9(t+1)
9 divides N
I do not understand this process. Can anyone show me the proof for the divisibility rule for 3?