Perfect power testing - Balasubramanian, R.; Nagaraj, S.V. (Information processing letters, 1996)
Bach and Sorenson present two algorithms for testing whether a number n is a perfect power, with average running time O( log 2 n) under the assumption that n is chosen uniformly from an interval of length at least ( log n) 3 log log log n . We modify their algorithms to reduce the interval to polynomial size.