Question

Show that one and only one out of n,n+1 and n+2 is divisible by 3, where n is any positive integer

Answer 1

n is an integer. So,it is of the form 3k,3k+1 or 3k+2 where k is an integer.

If n=3k,then

n+1=3k+1,not divisible by 3

n+2=3k+2,not divisible by 3

If n=3k+1(not divisible by 3),then

n+1=3k+2,not divisible by 3

n+2=3k+3=3(k+1), divisible by 3

If n=3k+2(not divisible by 3),then

n+1=3k+3=3(k+1),divisible by 3

n+2=3k+4=3(k+1)+1,not divisible by 3

Hence by seeing all the above cases,we can safely say that:out of n,n+1 and n+2,only one is divisible by 3.