# It's Hard To Find A Square

Number Theory Level 4

Let $$(m_1,n_1),(m_2,n_2),\ldots,(m_k,n_k)$$ be positive integer solutions of $$m$$ and $$n$$ such that $$m$$ is a perfect square and $$m=n^2+23n+175$$ is satisfied. If $$m_1 > m_2 > \ldots>m_k$$, find the value of $$\displaystyle \sum_{i=1}^k (-30)^{i-1} m_i n_i$$.

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