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

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

2011-12-16

arxiv.org/abs/1112.3820v2

Mathematics

Number Theory

22 pages, second version: minimal changes

Scientific paper

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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