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

Sources

The source's own material, retained exactly.

3 retained statements36c6d0fef71a

FormalConjectures/ErdosProblems/

325.lean

Retained formal statement3 of 3

For $k = 3$ , the best known is due to Wooley [Wo15] [Wo15] Wooley, Trevor D., Sums of three cubes, II. Acta Arith. (2015), 73-100.

FormalConjectures/ErdosProblems/325.leanErdos325.erdos_325.variants.wooley1 lineExact file

1(fun x => ↑x ^ 0.917) =O[Filter.atTop] fun x => ↑(Erdos325.cardIsSumThreePowerBelow 3 x)

SolvedStatement only, no proof