MathNet 2019-part-05 — 184 problems (EN–VI) Question 26

Show that for infinitely many positive integers $n$ there exist pairwise distinct positive integers $a_1, a_2, \dots, a_n$ such that $a_1^2 a_2^2 \cdots a_n^2 - 4(a_1^2 + a_2^2 + \cdots + a_n^2)$ is the square of an integer.