Prime Number has 4 Integral Divisors
Let $p$ be an integer.
Aiming for a contradiction, suppose:
- $\exists x < 0: x \divides p$
where $x \ne -1$ and $x \ne -p$.
- $\size x \divides x \divides p$
It follows that $p$ has exactly those four divisors.
Suppose $p$ has the divisors $1, -1, p, -p$.