Writing $28913000$ as the sum of two squares

Very good!

Do you know complex numbers? Assume that $-1$ has a square root somewhere (certainly not in $\mathbb R$), denote it $i$, and introduce $+$, $\cdot$ operations with reals and $i$. So, $i^2=-1$, thus $(a+bi)(a-bi) = a^2+b^2$. $$(a+bi)(a-bi)(c+di)(c-di) = (a+bi)(c+di)\cdot (a-bi)(c-di)$$ Can you calculate it?

You can easily check that $$ (a^2+b^2)(c^2+d^2)=(ac-bd)^2+(ad+bc)^2 $$