Question

Prove that one and only one out of $n,n+2$ or $n+4$ is divisible by $3$; where $n$ is any positive integer.

Answer 1

Let $n=1$

So $n+2=1+2=3$ and

$n+4=1+4=4$

$\therefore$ So $n+2$ is divisible by $3$

Let $n=2$

$n+2=2+2=4$

$n+4=2+4=6$

So $n+4$ is divisible by $3$.