IOM 2018 Problem 4

Let $1 = d_0 < d_1 < \dots < d_m = 4k$ be all positive divisors of $4k$ , where $k$ is a positive integer. Prove that there exists $i \in \{1, \dots, m\}$ such that $d_i - d_{i-1} = 2$ .

Ivan Mitrofanov