Let three consecutive positive integers are n, n + 1,
n + 2 respectively.
We know that n is of the form 3q or 3q + 1 or 3 q + 2.
Now following cases are possible.
Case 1.
when n = 3q which is divisible by 3
n + 1 = 3q + 1, Not divisible by 3
n + 2 = 3q + 2, Not divisible by 3
In this case n is divisible by 3 but (n + 1) and (n + 2) are not divisible by 3
Case 2.
When n = 3q + 1
In this positive Which is divisible by 3 but n and n + 1 are not divisible by 3.
Case 3.
When n = 3q + 2
In this position divisible by 3 but or (n + 2) are not divisible by 3
Hence out of n, (n + 1) and (n + 2) one is divisible by 3.
