Duke Mathematical Journal

Detecting squarefree numbers

Andrew R. Booker, Ghaith A. Hiary, and Jon P. Keating

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We present an algorithm, based on the explicit formula for L-functions and conditional on the generalized Riemann hypothesis, for proving that a given integer is squarefree with little or no knowledge of its factorization. We analyze the algorithm both theoretically and practically and use it to prove that several RSA challenge numbers are not squarefull.

Article information

Duke Math. J., Volume 164, Number 2 (2015), 235-275.

First available in Project Euclid: 30 January 2015

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Zentralblatt MATH identifier

Primary: 11Y16: Algorithms; complexity [See also 68Q25] 11M06: $\zeta (s)$ and $L(s, \chi)$
Secondary: 11Y35: Analytic computations 11M50: Relations with random matrices


Booker, Andrew R.; Hiary, Ghaith A.; Keating, Jon P. Detecting squarefree numbers. Duke Math. J. 164 (2015), no. 2, 235--275. doi:10.1215/00127094-2856619. https://projecteuclid.org/euclid.dmj/1422627048

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