Question

show that one and only one of n, n+2,n+4 is divisible by 3

Answer 1

let n=1,then the n, n+2,n+4 is divisible by 3

Answer 2

Case 1}
Let n be divisible by 3,
then (n+2)/3 = n/3 + 2/3...but 2 is not completely divisible by 3.
Therefore, (n+2) is not divisible by 3.
(n+4)/3 = n/3 + 4/3....but 4 is not completely divisible by 3.
Therefore, (n+4) is not divisible by 3.
Let n+2 be divisible by 3,

Case 2}
then n/3 = (n+2)/3 - 2/3...but 2 is not completely divisible by 3.
Therefore, n is not divisible by 3.
(n+4)/3 = (n+2)/3 + 2/3... again 2 is not completely divisible by 3.
Therefore, (n+4) is not divisible by 3.

Case 3}
Let (n+4) be divisible by 3,
then n/3 = (n+4)/3 - 4/3...but 4 is not completely divisible by 3.
Therefore, n is not divisible by 3.
(n+2)/3 = (n+4)/3 - 2/3...but 2 is not completely divisible by 3.
Therefore, (n+2) is not divisible by 3.