MathNet 2010 — Part 02 Question 134

Determine the least odd number $a \gt 5$ satisfying the following conditions: There are positive integers $m_1, m_2, n_1, n_2$ such that $a = m_1^2 + n_1^2$, $a^2 = m_2^2 + n_2^2$, and $m_1 - n_1 = m_2 - n_2$.