Sieve algorithms for perfect power testing

  title={Sieve algorithms for perfect power testing},
  author={Eric Bach and Jonathan P. Sorenson},
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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Publications referenced by this paper.
Showing 1-10 of 31 references

The Recognition Problem for the Set of Perfect Squares

SWAT • 1966
View 4 Excerpts
Highly Influenced

On the deterministic complexity of factoring polynomials over finite fields , lnjorm

E. C. Titchmarsh
Process . Lett . . • 1990

Parallel Algorithms for Shared-Memory Machines

Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity • 1990
View 3 Excerpts

Course notes for number theory and algorithms

J. Shallit
View 1 Excerpt