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arXiv · 1112.3820

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

H. A. Helfgott
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Abstract

Let f\in Z[x], deg(f)=3. Assume that f does not have repeated roots. Assume as well that, for every prime q, the inequality f(x)\not\equiv 0 mod q^2 has at least one solution in (Z/q^2 Z)^*. Then, under these two necessary conditions, there are infinitely many primes p such that f(p) is square-free.

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H. A. Helfgott. 2014-07-17. Square-free values of f(p), f cubic. https://arxiv.org/abs/1112.3820

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