Szemeredi's Theorem (Paperback)

High Quality Content by WIKIPEDIA articles In number theory, Szemeredi's theorem is a result that was formerly the Erd s-Turan conjecture (not to be confused with Erd s-Turan conjecture on additive bases). In 1936 Erd s and Turan conjectured for every value d called density 0 d 1 and every integer k there is a number N(d, k) such that every subset A of {1, ..., N} of cardinality dN contains a length-k arithmetic progression, provided N>N(d, k).