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 statement4 of 6

More concrete example for $f(n) = n^2 + 1$ , where the asymptote is $\sum_{n \le x} \tau(n^2 + 1) \sim \frac{3}{\pi} x \log x + O(x)$ . See Tao's blog [T].

FormalConjectures/ErdosProblems/975.leanErdos975.erdos_975.variants.n2_plus_1_strong1 lineExact file

1(fun x => Erdos975.Erdos975Sum (Polynomial.X ^ 2 + 1) x - 3 / Real.pi * x * Real.log x) =O[Filter.atTop] id

SolvedStatement only, no proof

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