Show that if 3 divides n^2, 3 divides n

[yaowang101]

Show that if 3 divides n^2, 3 divides n. Hint: n can only be in the form 3a, 3a + 1, 3a + 2

Can someone help me with this? It's pretty simple, I just don't know how to express it mathematically.

 

[mathman]

n² then has three possibilities.
9a²
9a²+6a+1
9a²+12a+4
Only the first (for n=3a) is divisible by 3. The other two have a remainder of 1 after division by 3.