Question

-Prove that one of any three consecutive positive
integer


must be

divisible by 3
​

Answer 1

Answer:

If n = 3p + 1, then n + 2 = 3p + 1 + 2 = 3p + 3 = 3(p + 1) is divisible by 3. So, we can say that one of the numbers among n, n + 1 and n + 2 is always divisible by 3. So there is always exactly one multiple of 3 among them.