Theorem

Szemeredi's Theorem

Number Theory

Any set of integers with positive upper density contains arbitrarily long arithmetic progressions. Proved by Endre Szemeredi, it generalizes the earlier Van der Waerden and Erdos-Turan results and underlies the later Green-Tao theorem.

Facts

Statement

A subset of the natural numbers with positive upper density contains an arithmetic progression of length k for every positive integer k. 1

Proof Year

1975 1

Classification

Statement Form

Existence Theorem 1

Connections

Source Szemeredi's Theorem (Wikipedia)

Sources

1. Szemeredi's Theorem (Wikipedia)

Wikimedia Foundation

Statement section, first sentence
Szemerédi's theorem asserts that a subset of the natural numbers with positive upper density contains an arithmetic progression of length k for all positive integers k.
lead paragraph, third sentence
Endre Szemerédi proved the conjecture in 1975.
Proved By: Endre Szemerédi, Lead
Endre Szemerédi proved the conjecture in 1975.

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Szemeredi's Theorem

Has Statement Form

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Proved By