# Teleporting button

Author: mathforces
Problem has been solved: 18 times

Русский язык | English Language

Lin invented a button that can teleport him to any point (on the same plane), at a distance of 1 meter. Lin used the button three times. Let $\frac{n}{m \cdot 2^k}$ be the probability that he is no more than a meter away from the initial point, where $(n, m) = 1$ and $n, m$ are odd positive integer numbers. Find the number of divisors of the number $(n + 1) (m + 1) (k + 1)$.