Claims

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2026_07_18_price: A GPT 5.6 Sol Pro argument submitted by Liam Price proves that a common prime at least i divides both binomial coefficients whenever j is at most 3i/2 or n = 2j, the two cases the site's curator credits on the problem page.

2026_07_25_van_doorn_rocca: Two unpublished 2026 manuscripts by Wouter van Doorn and Stefano Rocca prove that no counterexample has i = 1, 2 or i at least 1476, that each fixed i at least 4 allows only finitely many, and leave i = 3 open.

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