KnowraSchur's theoremLinked fromLinked fromThe 11 pages that link to Schur's theorem, each with the reason it gives.All 11Related 6Compared with 5Ramsey theoryRelated: It shows that coloring integers cannot eliminate every simple additive equation.Erdős–Szekeres theorem (monotone subsequences)Related: Its use of finite colorings and unavoidable patterns reflects a broader Ramsey-style viewpoint.Hales–Jewett theoremRelated: It is another arithmetic consequence in the same family of coloring arguments.Cameron–Erdős conjectureRelated: It shows that sum-free sets cannot occupy an entire color class indefinitely without additive constraints appearing.Friends and strangers theoremRelated: It is another Ramsey-style guarantee, but its unavoidable pattern is arithmetic rather than a triangle.Lonely runner conjectureRelated: Combinatorial methods related to Schur-type results enter some approaches to the conjecture.