Erdős problem 325 · problems.science

Writing $f_{k, 3}(x)$ for the number of integers $\leq x$ which are the sum of three $k$ th powers, is it true that $f_{k, 3}(x) \gg x ^ (3 / k)$ ?

Sources

Browse retained paths and inspect the exact material available for this Problem.

3 retained statements2415f78e850a

Open selected source

FormalConjectures/ErdosProblems/

325.lean

Retained formal statement2 of 3

Writing $f_{k, 3}(x)$ for the number of integers $\leq x$ which are the sum of three $k$ th powers, is it even true that $f_{k, 3}(x) \gg_{\epsilon} x ^ (3 / k - \epsilon)$ ?

FormalConjectures/ErdosProblems/325.leanErdos325.erdos_325.variants.weaker3 linesExact file

1True ↔2  ∀ ε > 0,3    ∀ (k : ℕ), 3 ≤ k → (fun x => ↑x ^ (3 / ↑k - ε)) =O[Filter.atTop] fun x => ↑(Erdos325.cardIsSumThreePowerBelow k x)

OpenStatement only, no proof

Sources

Search problems.science