Can someone explain what this paragraph is saying more clearly? 
In the last bullet, it says l must be even and provides an explanation. I don't understand the explanation, however. Why does it have to be even?

I don't really follow the argument given. Here's a correct argument...
If $a^2 = 2l$, then $a^2$ is divisible by 2. But 2 is prime, so $a$ must be divisible by 2 too - say $a = 2b$. Then $(2b)^2 = 2l$, i.e. $2b^2 = l$, and so $l$ is divisible by 2.
