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Sequences of integers exist with any possible upper density and lower density which do not contain an infinitely long arithmetic progression. Journal Information This monthly journal, begun in 1950, ...
https://doi.org/10.4169/amer.math.monthly.121.10.932 https://www.jstor.org/stable/10.4169/amer.math.monthly.121.10.932 The Monthly publishes articles, as well as ...
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