Question 1
Proof
Prove that for every natural number n ∈ N such that 3|n, the sum of the digits of n is divisible by 3.
Example
The sum of the digits of the number 4,128 is 4 + 1 + 2 + 8 = 15 = 3.5, and 4,128 = 3.1,376.
This is a useful tool for quickly determining whether a number is divisible by 3, but how can we be sure that it works for every natural number?