Erdős problem 494 · problems.science

Selfridge and Straus [SeSt58] also showed that the conjecture is true when 1) $k = 3$ and $|A| > 6$ or 2) $k = 4$ and $|A| > 12$ . More generally, they proved that $A$ is determined by $A_k$ (and $|A|$ ) if $|A|$ is divisible by a prime greater than $k$ .

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494.lean

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Similarly, Tao noted that the conjecture fails when $|A| = 2k$ , by taking $A$ to be a set of the total sum 0 and considering $-A$ .

FormalConjectures/ErdosProblems/494.leanErdos494.erdos_494.variants.card_eq_2k1 lineExact file

1∀ k > 2, ¬Erdos494.Erdos494Unique k (2 * k)

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