Question

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

Answer 1

Hey friend !!
Here is your solution

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 = 3q + 4 = 3 ( q + 1 ) + 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 and n +4 = 3q + 1 + 4 = 3 ( q + 1 ) + 2 is divisible by 3.

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

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