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 $f_{k, 3}(x) \gg x ^ (3 / k)$ ?

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3 retained statements2415f78e850a

FormalConjectures/ErdosProblems/

325.lean

Retained formal statement1 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 true that $f_{k, 3}(x) \gg x ^ (3 / k)$ ?

FormalConjectures/ErdosProblems/325.leanErdos325.erdos_3251 lineExact file

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

OpenStatement only, no proof