Erdős problem 975 · problems.science

For an irreducible polynomial $f \in \mathbb{Z}[x]$ with $f(n) \ge 1$ for sufficiently large $n$ , does there exists a constant $c = c(f) > 0$ such that $\sum_{n \le x} \tau(f(n)) \approx c \cdot x \log x$ ?

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6 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

975.lean

Retained formal statement6 of 6

The correctness of the growth rate is shown in [Va39] (lower bound) and [Er52b] (upper bound).

FormalConjectures/ErdosProblems/975.leanErdos975.erdos_975.variants.upper_bound4 linesExact file

1∀ (f : Polynomial ℤ),2  Irreducible f →3    (∀ᶠ (n : ℤ) in Filter.atTop, 1 ≤ Polynomial.eval n f) →4      Erdos975.Erdos975Sum f =O[Filter.atTop] fun x => x * Real.log x

SolvedStatement only, no proof

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