Let
$${f(x, k, d) = x(x + d)\cdots(x + (k - 1)d)}$$
be a polynomial with
$${k \geq 2}$$
,
$${d \geq 1}$$
. We consider the Diophantine equation
$${\prod_{i = 1}^{r} f(x_i, k_i, d) = y^2}$$
, which is inspired by a question of Erdős and Graham [4, p. 67]. Using the theory of Pellian equation, we give infinitely many (nontrivial) positive integer solutions of the above Diophantine equation for some cases.
