On a Generalization of Szemeredi's Theorem
Shkredov, I. D.
Original · EN
Let A [1,..,N]² be a set of cardinality at least N²/(log log N)ᶜ, where c>0 is an absolute constant. We prove that A contains a triple (k,m), (k+d,m), (k,m+d), where d>0. This theorem is a two-dimensional generalization of Szemeredi's theorem on arithmetic progression.
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