Find the minimum odd integer(positive) $\displaystyle a(>5)$such that:

(1)$\displaystyle a=m_1^2+n_1^2$ for some positive integers $\displaystyle m_1,n_1$.

(2)$\displaystyle a^2=m_2^2+n_2^2$ for some positive integers $\displaystyle m_2,n_2$.

(3)$\displaystyle m_1-n_1=m_2-n_2$.