Question 83
Let $\phi(n)$ denote the number of positive integers less than $n$ that are relatively prime to $n$ where $n$ is a positive integer. Find all pairs $(m, n)$ of positive integers satisfying
$$
2^n + (n - \phi(n) - 1)! = n^m + 1.
$$
$$
2^n + (n - \phi(n) - 1)! = n^m + 1.
$$