erdos_325

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

theorem erdos_325 :
     answer(sorry) ↔ ∀ k : ℕ, 3 ≤ k → (fun x : ℕ => (x : ℝ) ^ (3 / k : ℝ)) =O[atTop]
      (fun x : ℕ => (cardIsSumThreePowerBelow k x : ℝ))

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