Abstract
In this section, we discuss a conjecture of Erdős, which states that a set of natural numbers of positive lower density contains the sum of two infinite sets. We begin with the history of the conjecture and discuss its nonstandard reformulation. We then present a proof of the conjecture in the “high density” case, which follows from a “1-shift” version of the conjecture in the general case. We conclude with a discussion of how these techniques yield a weak density version of Folkman’s theorem.
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