A problem due to Martin Labar is to find a 3x3 magic square with 9 distinct perfect square entries or prove that such a magic square cannot exist. In this paper, I assume that such a magic square exists and show that the entries must have certain properties. This is accomplished using unique factorization in two different finite extensions of Z. One property that is proven is: no prime congruent to 3 modulo 8 can divide any entry.