Question 112
Let $n$ be an integer greater than $2$ and consider the set $A = \{2^n - 1, 3^n - 1, \dots, (n-1)^n - 1\}$. Given that $n$ does not divide any element of $A$, prove that $n$ is a square-free number. Does it necessarily follow that $n$ is a prime number?
Marius Bocanu
Marius Bocanu