galois.perfect_power¶
- galois.perfect_power(n)¶
Returns the integer base \(c > 1\) and exponent \(e > 1\) of \(n = c^e\) if \(n\) is a perfect power.
- Parameters
n (int) – A positive integer \(n > 1\).
- Returns
None
is \(n\) is not a perfect power. Otherwise, \((c, e)\) such that \(n = c^e\). \(c\) may be composite.- Return type
Examples
# Primes are not perfect powers In [1]: galois.perfect_power(5) # Products of primes are not perfect powers In [2]: galois.perfect_power(2*3) # Products of prime powers were the GCD of the exponents is 1 are not perfect powers In [3]: galois.perfect_power(2 * 3 * 5**3) # Products of prime powers were the GCD of the exponents is > 1 are perfect powers In [4]: galois.perfect_power(2**2 * 3**2 * 5**4) Out[4]: (150, 2) In [5]: galois.perfect_power(36) Out[5]: (6, 2) In [6]: galois.perfect_power(125) Out[6]: (5, 3)