Sieve algorithms for perfect power testing

@article{Bach1993SieveAF,
  title={Sieve algorithms for perfect power testing},
  author={Eric Bach and Jonathan P. Sorenson},
  journal={Algorithmica},
  year={1993},
  volume={9},
  pages={313-328}
}
A positive integern is a perfect power if there exist integersx andk, both at least 2, such thatn=x k . The usual algorithm to recognize perfect powers computes approximatekth roots fork≤log 2 n, and runs in time O(log3 n log log logn). First we improve this worst-case running time toO(log3 n) by using a modified Newton's method to compute approximatekth roots. Parallelizing this gives anNC 2 algorithm. Second, we present a sieve algorithm that avoidskth-root computations by seeing if the… CONTINUE READING
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