3. Conclusion
In this paper, we have shown that the answer to (Q1) is affirmative by Lemma 2,
while the answer to (Q2) is no by using Theorem 1. It seems that by Theorem 1,
the equation px + qy = z2 will have the unique solution (x, y, z) = (1, 1√p + q)
only when the sum of p and q is a perfect square. The answer to (Q2) can easily
be supported by a result of Sroysang (cf. [5]).