A Question About Euler's Factorization Method

Question

I'm trying to understand Euler's factorization method from this article: https://en.wikipedia.org/wiki/Euler%27s_factorization_method. What I don't understand is when the article states "As each factor is a sum of two squares, one of these must contain both even numbers: either (k,h) or (l,m)". Why does the fact that each factor is a sum of two squares, mean one of these must contain both even numbers?

Answer 1

I think the key to recognizing that either (k,h) or (l,m) must be even is to recognize that either factor must be an integer multiple of 4. That is, either $(k^2 + h^2)$ or $(l^2 + m^2)$ must be divisible by 4. This means either (k,h) or (l,m) must be divisible by 2 and thus even.