divisibility - Proof if $n$ is divisible by $3$ then the sum of the digits of $n$ are a multiple of $3$

Proof if $n$ is divisible by $3$ then the sum of the digits of $n$ are a multiple of $3$. What is the name of that theorem and who performed that theorem?
I don't understand the proof given here: How to Prove the divisibility rule for $3$