Number theory/ divisibility

1. Sep 16, 2010

alexfresno

{SOLVED}Number theory/ divisibility

Show that m^2 is divisible by 3 if and only if m is divisible by 3.

MY attempt:

I assumed that 3k=m for some integers k and m.
squared both sides and now get.

3n=m where n=3*(3k^2). Thus 3|m^2

Now the problem is when i assume:
3k=m^2 and need to show 3|m.

Last edited: Sep 16, 2010
2. Sep 16, 2010

snipez90

The easiest way seems to be via contradiction. If 3k = m^2 but 3 does not divide m, then what do you know about the prime factorization of m^2?