Cube of Prime has 4 Positive Divisors

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Theorem

Let $n \in \Z_{>0}$ be a positive integer which is the cube of a prime number.


Then $n$ has exactly $4$ positive divisors.


Proof

Let $n = p^3$ where $p$ is prime.

The positive divisors of $n$ are:

$1, p, p^2, p^3$



Sources