Investigate "Detecting perfect powers in essentially linear time" Bernstein 1998, "Detecting perfect powers by factoring into coprimes." Bernstein, Lenstra, Pila 2007 & GMP for perfect power detection

[huonw]

• http://cr.yp.to/arith.html#powers & powers2
• https://gmplib.org/manual/Perfect-Power-Algorithm.html