Claims

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1984_02_01_erdos_freud: Erdős and Freud (J. Number Theory 1984) answer the question in the negative with the integers using only even, respectively only odd, powers of two, for which liminf min(A(x), B(x))/sqrt(x) = 1/sqrt(2); refereed.

2024_06_19_ruzsa: Numbers with binary digits only in even places and numbers with binary digits only in odd places each grow like the square root of N, yet every n has at most one representation a + b, so no nonzero common difference.

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