Erdős problem 829 · problems.science

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 $n \to \infty$ ?

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9 retained statements2415f78e850a

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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

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