Prime Number has 4 Integral Divisors

Theorem
Every prime number $$p$$ has exactly four integral divisors: $$1, -1, p, -p$$.

Proof

 * From the definition of a prime number, $$1$$ and $$p$$ divide $$p$$.

Also, we have $$-1 \backslash p$$ and $$-p \backslash p$$ from Integer Divisor Results.


 * Now suppose $$x < 0: x \backslash p$$ where $$x \ne -1$$ and $$x \ne -p$$.

Then $$\left|{x}\right| \backslash x \backslash p$$ and $$\left|{x}\right|$$ is therefore a positive integer other than $$1$$ and $$p$$ that divides $$p$$, which is a contradiction of the conditions of $$p$$ being a prime.

So $$-1$$ and $$-p$$ are the only negative integers that divide $$p$$, and the result follows.