On a Generalization of Szemeredi's Theorem
I. D. Shkredov
Abstract
Let A ⊂eq [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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