Real No.s

suppose n is divisible by 3

 i.e.

 n is a multiple of 3, then the next multiple of 3 will be n+3, then after that n+6... and so on..

so if n is a multiple of 3 then n+2 and n+4 can't be multiples of 3, so we have proved the required.

 similarly,

 if n+2 is a multiple of 3, then the multiple before that would be n-1, and the one after n+2 would be n+5

so if n+2 is a multiple of 3 then neither n nor n+4 can be a multiple of 3, so we have proved it again.

 you can prove the third part similarly.