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 in time O(N^{1/4r+epsilon }) for any epsilon > 0. For example, the algorithm can be used to test squarefreeness of N in time O(N^{1/8+epsilon }); previously, the best rigorous bound for this problem was O(N^{1/6+epsilon }), achieved via the Pollard–Strassen method.
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