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 statement3 of 9

The Hardy-Ramanujan taxicab number satisfies $1729 = 1^3 + 12^3 = 9^3 + 10^3$ , giving the four ordered representations $(1, 1728), (1728, 1), (729, 1000), (1000, 729)$ .

FormalConjectures/ErdosProblems/829.leanErdos829.sumRep_cubes_taxicab1 lineExact file

1AdditiveCombinatorics.sumRep Erdos829.cubes 1729 = 4

TestStatement only, no proof

Source providers

Erdős Problems1
locator only
Formal Conjectures9
statement retained
VibeMathed0
not observed here
PLBY Lean proofs0
not observed here
Jayyhk Erdős Lean0
not observed here
William Blair Lean proofs0
not observed here
Erdős AI contributions wiki0
not observed here
GPT-Erdős0
not observed here

Referenced paths

FormalConjectures/
- ErdosProblems/
  - 829.lean9