Question

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

Answer 1

We know that any integer is of form n=3q,3q+1,3q+2.
Case1:
When n=3q,
n=3q..... divisible by 3.
n+2=3q+2...not divisible
n+4=3q+4....not divisible
Case2:
When n=3q+2
n=3q+2 .....not divisible by3
n+2=3q+2+2=3q+4....not divisible
n+4=3q+2+4=3q+6.... divisible
Similarly Case 3 of n=3q+1.

Answer 2

hope this is proof u need dear