Question 68
Let $n$ be a natural number whose all positive divisors are denoted as $d_1, d_2, \dots, d_k$ in such a way that $d_1 \lt d_2 \lt \dots \lt d_k$ (thus $d_1 = 1$ and $d_k = n$). Determine all the values of $n$ for which both equalities $d_5 - d_3 = 50$ and $11d_5 + 8d_7 = 3n$ hold. (Matúš Harminc)