Claims

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1974_02_14_erdos_szemeredi: Erdős and Szemerédi (Publ. Math. Debrecen, 1976) prove Graham's conjecture for p nonzero residues modulo every sufficiently large prime p; refereed, credited by the site, and partial: small primes and the residue 0 are left.

2009_02_27_gao_hamidoune_wang: Theorem 1.1 of Gao, Hamidoune and Wang (J. Number Theory, 2010): n integers in [0, n-1] taking at least three values have two nonempty zero-sum subsequences modulo n of distinct lengths; refereed, credited by the site.

2009_03_18_grynkiewicz: Theorem 3.4 of Grynkiewicz (European J. Combin., 2011): a sequence of n elements of a finite abelian group of order n whose nonempty zero-sum subsequences all have one length has at most two distinct terms; refereed.

2025_12_31_alexeev: A Lean 4 proof of the prime-modulus statement, produced by Boris Alexeev with Aristotle and ChatGPT and posted in the site's thread on 31 December 2025; a later revision was built and audited by this corpus, so accepted.

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