Question 170
Prove that for every prime number $p$ there exist infinitely many 4-tuples $(x, y, z, t)$ of pairwise distinct positive integers such that the number
$$
(x^2 + pt^2)(y^2 + pt^2)(z^2 + pt^2)
$$
is a square of an integer.
$$
(x^2 + pt^2)(y^2 + pt^2)(z^2 + pt^2)
$$
is a square of an integer.