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Creators/Authors contains: "Hittmeir, Markus"

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  1. ; (, Research in Number Theory)
    Abstract Building on work of Boneh, Durfee and Howgrave-Graham, we present a deterministic algorithm that provably finds all integers p such that $$p^r \mathrel {|}N$$ p r | N in time $$O(N^{1/4r+\epsilon })$$ O ( N 1 / 4 r + ϵ ) for any $$\epsilon > 0$$ ϵ > 0 . For example, the algorithm can be used to test squarefreeness of N in time $$O(N^{1/8+\epsilon })$$ O ( N 1 / 8 + ϵ ) ; previously, the best rigorous bound for this problem was $$O(N^{1/6+\epsilon })$$ O ( N 1 / 6 + ϵ ) , achieved via the Pollard–Strassen method. 
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