The divisibility rule by 3 is a rule that a number N is divisible by 3 if the sum of the digits is divisible by 3. For example, is 132 divisible by 3? 1+3+2=6 and 6 is a number divisible by 3. So 132 must also be divisible by 3. Please prove this "rule" for three digit numbers: Let the positive integer N have the form N= 100a+10b+c where a+b+c= 3n and a, b, and care digits with a 0. Prove that N is divisible by 3.