Roth's theorem on arithmetic progressions
GPTKB entity
Statements (16)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:field |
number theory
additive combinatorics |
| gptkbp:generalizes |
gptkb:van_der_Waerden's_theorem
|
| gptkbp:hasSpecialCase |
gptkb:Szemerédi's_theorem
|
| https://www.w3.org/2000/01/rdf-schema#label |
Roth's theorem on arithmetic progressions
|
| gptkbp:implies |
no large subset of integers is free of 3-term arithmetic progressions
|
| gptkbp:namedAfter |
gptkb:Klaus_Roth
|
| gptkbp:provenBy |
gptkb:Klaus_Roth
|
| gptkbp:publishedIn |
gptkb:Proceedings_of_the_London_Mathematical_Society
|
| gptkbp:state |
Any subset of the integers from 1 to N with positive density contains a nontrivial 3-term arithmetic progression for sufficiently large N.
|
| gptkbp:topic |
arithmetic progressions
density of sets of integers |
| gptkbp:yearProved |
1953
|
| gptkbp:bfsParent |
gptkb:Roth's_theorem
|
| gptkbp:bfsLayer |
7
|