单词

Szemerédi's theorem

释义

Szemerédi's theorem

The theorem shows that a suitably dense subset of the natural numbers contains arbitrarily long arithmetic progressions. The set A ⊆ ℕ needs to satisfy

The theorem implies Van der Waerden's theorem but does not imply the Green-Tao theorem, as the primes do not have positive density. See also Erdős conjecture.

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