Let a and b be a natural numbers such that a2 = b3. Prove the following proposition:
If a is even, then 4 divides a.
Definition: A nonzero integer m divides an integer n provided that there is an integer q such that n = m * q.
Definition: A even number m can be represented by the relationship m = 2 * n where n is an integer.
The Attempt at a Solution
Let a = 2n where b is any integer. Let b = 2m where m is any integer (from another theorem, the cube of any even is even).
a^2 = b^3
(2n)(2n) = 8m^3
2n = 4m^3/n
I am not even sure if I did all of the above correctly; but, this is as far as I got.