MathNet 2015-part-05 — 191 problems (EN–VI) Question 61

Show that there are positive odd integers $m_1 \lt m_2 \lt \dots$ and positive integers $n_1 \lt n_2 \lt \dots$ such that $m_k$ and $n_k$ are relatively prime, and $m_k^4 - 2n_k^4$ is a perfect square for each index $k$.