Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
finite sets of complex numbers
finite sets of integers finite sets of real numbers |
| gptkbp:field |
number theory
combinatorics additive combinatorics |
| gptkbp:hasConjecture |
For any finite set A of integers, max(|A+A|, |A·A|) ≥ c|A|^{1+ε} for some ε>0 and constant c>0.
|
| https://www.w3.org/2000/01/rdf-schema#label |
sum-product problem
|
| gptkbp:introduced |
gptkb:Paul_Erdős
gptkb:Endre_Szemerédi |
| gptkbp:introducedIn |
1983
|
| gptkbp:notableAchievement |
Erdős–Szemerédi theorem gives lower bounds for sum and product sets.
|
| gptkbp:notableContributor |
gptkb:József_Solymosi
gptkb:Terence_Tao gptkb:Giorgis_Petridis |
| gptkbp:relatedConcept |
gptkb:Erdős–Szemerédi_theorem
product set sum set |
| gptkbp:status |
open problem
|
| gptkbp:type |
How small can the sum set and product set of a finite set of numbers be?
|
| gptkbp:bfsParent |
gptkb:Erdős–Szemerédi_theorem
|
| gptkbp:bfsLayer |
5
|