1. The problem statement, all variables and given/known data Assume a is a natural number and that a^2 is divisible by 3 (that is, there exists natural number n so that 3n = a^2) 2. Relevant equations 3. The attempt at a solution I thought about doing this one by contradiction. Suppose a is not divisible by 3. Then a/3 can be written as a/3 = b/c where b and c are natural numbers with no common factors. From there I square both sides to get (a^2)/9 = b^2/c^2 My plan was to then show that this implies (a^2)/3 is NOT a natural number, a contradiction, which would imply no such b and c exist. I'm not certain if this is the right angle, however, since I had a hard time justifying that 3(b^2)/c^2 is not a natural number.