MathNet 2016-part-06 — 184 problems (EN–VI) Question 53

If $n$ is a natural number, the $n$-th triangular number is $T_n = 1 + 2 + \cdots + n$. Find all values of $n$ for which the product of the 16 consecutive triangular numbers $T_n T_{n+1} \cdots T_{n+15}$ is a perfect square.