# A number theory problem by Nick Okita

Number Theory Level 5

$\large p^n + 144 = q^2$

Let $$p,q$$ and $$n$$ be positive integers satisfying the equation above such that $$p$$ is a prime number. Let all the solutions of $$(n,p,q)$$ be denotes as $$(n_1, p_1, q_1) , (n_1, p_1, q_1) , \ldots , (n_m, p_m, q_m)$$. Find $$\displaystyle \sum_{k=1}^m (n_k + p_k + q_k )$$.

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