A Note on the Diophantine Equation pˣ + (p + 1)ʸ = z²

proved that the equation p x + (p + 1) y = z 2 has the unique solution (p, x, y, z) = (3, 1, 0, 2) when p is an odd prime and x, y, z are non-negative integers. In this note, we refute the uniqueness of this solution by presenting a counter-solution. When p = 2 is added to the list of odd primes, two solutions of the equation are demonstrated. Finally, when the prime p is substituted by a composite C, then from [4] it follows that the equation has exactly two such solutions which are exhibited.