galois.is_prime_power

galois.is_prime_power(n: int) → bool

Determines if $n$ is a prime power $n = p^{k}$ for prime $p$ and $k \geq 1$ .

Parameters:¶

n: int¶: An integer.

Returns:¶

True if the integer $n$ is a prime power.

See also

is_perfect_power, is_prime

Notes¶

There is some controversy over whether 1 is a prime power $p^{0}$ . Since 1 is the 0-th power of all primes, it is often regarded not as a prime power. This function returns False for 1.

Examples¶

In [1]: galois.is_prime_power(8)
Out[1]: True

In [2]: galois.is_prime_power(6)
Out[2]: False

In [3]: galois.is_prime_power(1)
Out[3]: False