Open. The site credits Prikry, Tijdeman, Stewart and others with the sufficient condition that $A$ has positive density. Theorem 2 of Stewart and Tijdeman (Canad. J. Math. 1979, refereed) proves that positive upper density suffices, the accepted partial claim on its claim page (Stewart Tijdeman, 1979); Prikry's independent proof, which they cite as a private communication, was not published and has no page. A note linked from the thread on 4 May 2026, posted as an observation by GPT 5.5 pro, claims positive upper Banach density, a pending partial claim on its claim page (aditya, 2026).