pn+144=q2
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 (n1,p1,q1),(n2,p2,q2),…,(nm,pm,qm). Find k=1∑m(nk+pk+qk).
This question was taken from IME (Instituto Militar de Engenharia) 2009-2010 entrance exam.