Claims

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1975_03_01_baumgartner: One element of each infinite arithmetic progression, chosen beyond twice the previous choice, gives a Sidon set meeting every progression; the site credits Baumgartner, whom Erdős and Graham credit with the answer yes.

2025_05_15_deepmind: The set of the numbers (n+1)!+n is Sidon and meets every infinite arithmetic progression; found by Google DeepMind's AlphaProof, written out on the site's page and formalized in Lean by Alexeev with Aristotle in November 2025.

2025_09_02_dutta: For every x outside a meager subset of the reals above 2, the integer parts of the powers of x form a Sidon set meeting every infinite arithmetic progression; a Baire-category argument posted in the site's thread in 2025.

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