A third update on my previous posts https://mathstodon.xyz/@tao/115306424727150237 https://mathstodon.xyz/@tao/115316787727719049 https://mathstodon.xyz/@tao/115325228243131134 on the #MathOverflow problem https://mathoverflow.net/questions/501066/is-the-least-common-multiple-sequence-textlcm1-2-dots-n-a-subset-of-t . Out of curiosity, I asked an AI deep research tool for the known literature on this problem: https://g.co/gemini/share/0d41fcadfbaf . As is often the case with these frontier models, the results were mixed. On the one hand, the tool correctly identified a relevant paper of Alaoglu and Erdos from 1944 https://users.renyi.hu/~p_erdos/1944-03.pdf , where they claimed that the authors knew that the conjecture was false, but did not provide a proof. The AI then hallucinated by asserting that n=17 was a counterexample, which I knew to be false. Based on this latter failure, I did not initially give much credence to the initial statement; but later, after reading the Alaoglu-Erdos paper carefully, I did find (on pages 466-467) that they did indeed make the observation that "it would be easy to see" that the conjecture could only be true finitely often, without providing any hint of a proof. (1/4)