Question 63
Let $N$ be an integer greater than $1$. Let $x$ be the smallest positive integer with the following property: there exists a positive integer $y$ strictly less than $x-1$ such that $x$ divides $N+y$. Prove that $x$ is either twice a prime number or a power of a prime number.
Note: recall that $x$ is a power of a prime number if there exist a prime $p$ and a positive integer $n \geq 1$ such that $x=p^{n}$.
Note: recall that $x$ is a power of a prime number if there exist a prime $p$ and a positive integer $n \geq 1$ such that $x=p^{n}$.