Question

show that exactly one of the number n,n + 2 or 1 + 4 is divisible by 3

Answer 1

Hello mate !!
Here is your solution

First of all there is correction in your question.
I think your question should be like this :-
Show that exactly one number n, n+2 and n + 4 is divisible by 3.

So your solution is as follows :-

Let n be any positive integer. Then
n = 3q or 3q +1 or 3q +2

If n = 3q
Then , n= 3q is divisible by 3
n +2 = 3q +2 is not divisible by 3
and also n + 4 = 3 ( q +1 ) is not divisible by 3

If n = 3q + 1
Then n = 3q + 1 is not divisible by 3
n +2 = 3q + 1 + 2= 3( q +1 ) is divisible by 3
n +4 = 3q + 1 + 4 = 3 ( q + 1 ) + 2 is not divisible by 3.

if n = 3 q + 2
then , n = 3q +2 is not divisible by 3
n + 2 = 3q + 2+ 2 = 3( q + 1 ) + 1 is not divisible by 3.
n + 4 = 3q + 2 + 4 = 3 ( q + 2 ) is divisible by 3.

Thus only one out of n, n+2 and n +4 is divisible by 3.

Hope this will help you :)
All the best for exam

Answer 2

Here is ur answer....
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