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 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