Products of Arithmetic Progressions which are Squares

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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).

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