Question

Show that exactly one of the numbers n, n+2or n+4 is divisible by 3

Answer 1

Since n is a positive integer taking b =3

We can write n = 3q + r , where q is some integer

n = 3q , n = 3q + 1 , n = 3q + 2

Case 1 = When n = 3q, n + 2 = 3q + 2 and n + 4 = 3q + 4 clearly only 3q is divisible by 3

Case 2 = When n = 3q + 1, n + 2 = 3q + 3 and n + 4 = 3q + 5 .

Here also only n + 2 = 3q + 3 = 3(q + 1) is divisible by 3. Other two namely n and n + 4 are not divisible by 3

Case 3 = When n = 3q + 2, n + 2 = 3q + 4 and n + 4 = 3q + 6 and in this case, only n + 4 = 3(q + 2) is divisible by 3

Hence only one out of n, n + 2 and n + 4 is divisible by 3 for any positive integer n .

Answer 2

Answer:

Step-by-step explanation:take n= 1

Then n=1 not divisible by 3

n+2= 3 divisible by 3

n+4 =5 not divisible by 3