If n is an integer, show that one of the integers n, n+2, or n+4 is divisible by 3.

If n is an integer, show that one of the integers n, n+2, or n+4 is divisible by 3.

solution:
If n is a multiple of 3, then there is nothing more to prove.

Suppose n is not a multiple of 3, then n must be of the form
n =3k+1 or n = 3k+2, for some integer k

if n=3k+1,
then n+2 = (3k+1)+2 = 3k+3 = 3(k+1) = multiple of 3

if n = 3k+2,
then n+4 = 3k+6 = 3(k+2) =multiple of 3


hence the result

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