Acta Mathematica

Square-free values of f(p), f cubic

Harald Andrés Helfgott

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Let fZ[x], degf=3. Assume that f does not have repeated roots. Assume as well that, for every prime q, f(x)0 mod q2 has at least one solution in (Z/q2Z). Then, under these two necessary conditions, there are infinitely many primes p such that f(p) is square-free.

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Acta Math., Volume 213, Number 1 (2014), 107-135.

Received: 29 June 2012
Revised: 28 May 2013
First available in Project Euclid: 30 January 2017

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2014 © Institut Mittag-Leffler


Helfgott, Harald Andrés. Square-free values of f ( p ), f cubic. Acta Math. 213 (2014), no. 1, 107--135. doi:10.1007/s11511-014-0117-2.

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