Erdős problem 1097 · problems.science

The main conjecture: for any finite set of integers $A$ with $|A| = n$ , the number of distinct common differences in three-term arithmetic progressions is $O(n^{3/2})$ .

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FormalConjectures/ErdosProblems/

1097.lean

Retained formal statement2 of 3

A trivial lower bound: for sufficiently large n there exist sets $A$ with $|A| = n$ that contain at least $\Omega(n)$ distinct common differences of three-term arithmetic progressions.

FormalConjectures/ErdosProblems/1097.leanErdos1097.erdos_1097.variants.lower_bound1 lineExact file

1∃ c > 0, ∀ᶠ (n : ℕ) in Filter.atTop, ∃ A, A.card = n ∧ c * ↑n ≤ ↑(Erdos1097.CommonDifferencesThreeTermAP A).ncard

TextbookStatement only, no proof

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