Problems need HardWork #16

Since the problem is phrased so as to assume there must a unique solution for $n$ , and since $p=5, a=280,$ and $n=1$ satisfies the equality, then $1$ must be the unique solution.

Let $p=2$ then $2^2 + 3^2 = 9 + 4 = 13$ Since $a$ and $n$ are both integers there is only one valid solution $a = 13$ and $n = 1$ Based of the phrasing it can be assumed this is the only solution.