Question 4
Let $n \in \mathbb{N}$ be such that $n^3 + 1$ is divisible by $56$, and $d_1^6 + d_2^6 + \dots + d_k^6$ is divisible by $112$, where $d_1, d_2, \dots, d_k$ are all the positive divisors of $n$. Which is the smallest amount of divisors that $n$ can have?