Claims

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1996_12_02_erdos_sarkozy: Erdős and Sárközy prove that for large n a set above the triangle threshold has every odd cycle of length up to 2cn+1 in its coprime graph, for some unspecified c > 0; a weaker form of the first question.

1999_05_01_sarkozy: Theorem 1 of Sárközy (Discrete Math. 1999) gives, for large n, a complete (1, l, l) subgraph with l of order log n / log log log n in the coprime graph of any set above the triangle threshold; the second question.

2026_07_27_della_pietra: Della Pietra's manuscript and Lean development claim the first question of Problem 883 for all sufficiently large n, every odd cycle of length at most n/3+1 above the triangle threshold, with 1/6 sharp; unreviewed.

2026_10_05_pan: Pan's manuscript and Lean development claim the first question of Problem 883 for every n, by an analytic argument from n = 200000 on and finite certificates below; the second question is not addressed; unreviewed.

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