$n_1={m_1}^2+{m_2}^2+{m_3}^2+{m_4}^2$, $n_2={k_1}^2+{k_2}^2+{k_3}^2+{k_4}^2$, so we have $n_1n_2={l_1}^2+{l_2}^2+{l_3}^2+{l_4}^2$. How to find $l_i$?

Question

$n_1={m_1}^2+{m_2}^2+{m_3}^2+{m_4}^2$, $n_2={k_1}^2+{k_2}^2+{k_3}^2+{k_4}^2$, so we have $n_1n_2={l_1}^2+{l_2}^2+{l_3}^2+{l_4}^2$. How to find $l_i$? I remember I read something about this, but don't remember what is this. Can anyone can tell or show me some material about this question?

Answer 1

It's another of Euler's formulas: Euler's four square identity