Erdős problem 829

Erdős Problem 829 (open). Let $A \subseteq \mathbb{N}$ be the set of perfect cubes. Is it true that $(1_A \ast 1_A)(n) \ll (\log n)^{O(1)}$ ? That is, does there exist a natural number $C$ such that the number of representations of $n$ as a sum of two cubes is $O((\log n)^C)$ as $n \to \infty$ ?

Sources

The source's own material, retained exactly.

9 retained statements36c6d0fef71a

FormalConjectures/ErdosProblems/

829.lean

Retained formal statement2 of 9

Membership in cubes can be witnessed by a bounded cube root, which makes it decidable for concrete values.

FormalConjectures/ErdosProblems/829.leanErdos829.mem_cubes_iff1 lineExact file

1∀ (m : ℕ), m ∈ Erdos829.cubes ↔ ∃ k < m + 1, k ^ 3 = m

APIStatement only, no proof