Products of Arithmetic Progressions which are Squares

In this short note, we shall give a result similar to Y. Zhang and T. Cai [5] which states the diophantine equation

(x − b)x(x + b)(y − b)y(y + b) = z2

has infinitely many nontrivial positive integer solutions (x, y, z) when b(≥ 2) is even. We shall show this diophantine equation also has infinitely many nontrivial positive integer solutions when integers b is divisible by a prime p(≡ ±1 mod 8).