Claims

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2026_07_16_sawin: Sawin's 2026 preprint constructs positive-density subsets of the first N integers in which the sum of two distinct members never divides twice their product, a negative answer to the second question; unreviewed, pending.

2026_07_29_della_pietra: A full, AI-assisted claim of 29 July 2026 by Donald Della Pietra that sets in which a + b never divides ab can exceed the odd numbers by a positive proportion of N, with a reproof of the second question; not accepted.

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