Problem 325

Erdős Problem #325: declared status 'open'. Formalized: yes. Let $k\geq 3$ and $f_{k,3}(x)$ denote the number of integers $\leq x$ which are the sum of three nonnegative $k$th powers. Is it true that$$f_{k,3}(x) \gg x^{3/k}$$or even $\gg_\epsilon x^{3/k-\epsilon}$? Current best: For $k=3$ the best known is due to Wooley [Wo15],$$f_{3,3}(x) \gg x^{0.917\cdots}.$$This problem has been formalised in Lean as part of the Google DeepMind Formal Conjectures project. Prize: no. Tags: number theory, powers.