Unity Is Strength

The two numbers a and b will have to be of the form of 3n+1 and 3k+2 respectively. (Since they give different non-zero remainders when divided by 3; here n and k are whole numbers)

Thus, a + b= 3(n+k) + 1 + 2 = 3(n+k+1), which is always divisible by 3.

Let $a=2$ and $b=4$ . Then

• 2 and 4 are two distinct positive integers which are not divisible by 3. True
• When $a$ and $b$ are divided by 3 their remainders are 2 and 1 respectively which are not the same. True
• $2+4$ is also not divisible by 3. False

If a and b are not divisible by 3 and their remainders on being divided by 3 are also different,

Then a = 3m+1. and b=3n+2

Or vice versa

a + b = 3m+3n+ 1+ 2

      = 3(m+n+1)

Hence, it is divisible by 3.