Claims

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1979_10_01_stewart_tijdeman: Stewart and Tijdeman's 1979 Theorem 2: for a set of positive upper density, finitely many translates of its set of differences occurring infinitely often cover the non-negative integers, so that set has bounded gaps; refereed.

2026_05_04_aditya: A note linked from the Problem 332 thread on 4 May 2026 proves that the differences occurring infinitely often have bounded gaps for every set of positive upper Banach density; posted as an observation by GPT 5.5 pro.

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