Question

Prove or disprove the following: If the integer n is divisible by 3 then n^2 is divisible by 3. Use the direct method of proof as outlined in the notes.

Answer 1

If n is divisible by 3, it can be written 3a, where a is an integer.

n^2 = 9 a^2, where a^2 is also an integer, is also divisible by three, since 9 = 3 x 3.

I don't have your notes so have no idea what kind of proof they expect.