Question

Show that one and one out of n, n+2or n+4 is divisible by 3, where n is any positive integer

Answer 1

Given numbers,

n , n+2 and n+4

{n is any positive integer}

» If n = 1,

n = 1
n+2 = 1+2 = 3 is divisible by 3
n+4 = 1+4 = 5

» If n = 2,

n = 2
n+2 = 2+2 = 4
n+4 = 1+4 = 6 is divisible by 3

» If n = 3,

n = 3 is divisible by 3
n+2 = 3+2 = 5
n+4 = 3+4 = 7

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