Claims

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1994_09_01_sarkozy_szemeredi: Sárközy and Szemerédi (Acta Math. Hungar. 1994) prove that infinite additive complements with A(x)B(x) ~ x have A(x)B(x) - x tending to infinity, not even o(A(x)); accepted, refereed and credited by the site.

2010_02_05_fang_chen: Fang and Chen (Proc. Amer. Math. Soc. 2010) prove that infinite A, B with A + B covering all large integers and limsup A(x)B(x)/x < 5/4 have A(x)B(x) - x tending to infinity; accepted, refereed and credited by the site.

2014_08_01_fang_chen: Fang and Chen (J. Number Theory 2014) prove that infinite A, B with A + B covering all large integers and limsup A(x)B(x)/x < 3 - sqrt(3) have A(x)B(x) - x tending to infinity; accepted, refereed and credited by the site.

2015_01_01_chen_fang: Theorem 0.2 of Chen and Fang (Acta Arith. 2015): for infinite additive complements with limsup A(x)B(x)/x at most 1, A(x)B(x) - x is at least min(A(x),B(x))^M for every M > 1; accepted, refereed and credited by the site.

2015_10_03_ruzsa: Ruzsa (Q. J. Math. 2017) proves A(x)B(x) - x > (1 - o(1)) a*(x)/A(x) for exact additive complements, which reproves the problem; accepted, refereed and credited by the site; van Doorn's 2026 Lean proof is linked, not built.

2026_08_05_van_doorn_liu_tang: A proof claim of 2026-08-05 that infinite additive complements with limsup A(x)B(x)/x < 3/2 have A(x)B(x) - x tending to infinity, Chen's conjecture; note by GPT-5.6 Sol, Lean by Aristotle, no review recorded.

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