Browsing Pure Mathematics by Subject "Additive combinatorics"

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A survey of Roth's Theorem on progressions of length three

Nishizawa, Yui (University of Waterloo, 2011-12-19)

For any finite set B and a subset A⊆B, we define the density of A in B to be the value α=|A|/|B|. Roth's famous theorem, proven in 1953, states that there is a constant C>0, such that if A⊆{1,...,N} for a positive integer ...