Question

Prove that one of every three consecutive positive integers is divisible by 3.

Answer 1

Let n be any positive integer.

∴ n = 3q + r, where r = 0, 1, 2

Putting r = 0,

n = 3q + 0 = 3q, which is divisible by 3.

Putting r = 1,

n = 3q + 1, which is not divisible by 3.

Putting r = 2,

n = 3q + 2, which is not divisible by 3.

Hence, one of every three consecutive positive integers is divisible by 3.

Hence Proved.