Cube of Prime has 4 Positive Divisors

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:

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

This result follows from Divisors of Power of Prime.

$\blacksquare$

Sources

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $33$