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## Homework Statement

Let a and b be a natural numbers such that a

^{2}= b

^{3}. Prove the following proposition:

*If a is even, then 4 divides a.*

## Homework Equations

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.