Suppose that $m_1,m_2,m_3,n_1,n_2,n_3 \in \mathbb N$ and $m_1<m_2<m_3$ and $n_1<n_2<n_3$.
If $\dfrac {{n_1}^2+{n_2}^2+{n_3}^2-3}{{m_1}^2+{m_2}^2+{m_3}^2-3}$ is a natural number,
do we then neccessarily have ${n_1}^2+{n_2}^2+{n_3}^2={m_1}^2+{m_2}^2+{m_3}^2$?