Erdős conjecture on arithmetic progressions

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Statement

Every large set of natural numbers, i.e., every subset of the set of natural numbers whose sum of reciprocals diverges, contains aribtrarily long arithmetic progressions.

Relation with other facts/conjectures

Weaker facts

Name Statement Proof of implication
Green-Tao theorem This states that the set of primes contains arbitrarily long arithmetic progressions set of primes is large
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