Erdős problem 323 · problems.science

Is it true that $f_{k,k}(x) \gg_\epsilon x^{1-\epsilon}$ for all $\epsilon>0$ ?

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4 retained statements2415f78e850a

FormalConjectures/ErdosProblems/

323.lean

Retained formal statement1 of 4

Is it true that $f_{k,k}(x) \gg_\epsilon x^{1-\epsilon}$ for all $\epsilon>0$ ?

This would have significant applications to Waring's problem. Erdős and Graham describe this as 'unattackable by the methods at our disposal'.

FormalConjectures/ErdosProblems/323.leanErdos323.erdos_323.parts.i1 lineExact file

1True ↔ ∀ k ≥ 1, ∀ ε > 0, (fun x => ↑x ^ (1 - ε)) =O[Filter.atTop] fun x => ↑(Erdos323.f k k x)

OpenStatement only, no proof