IMO 1986 LL CHN15

Let N = B1 \cup\cdot \cdot \cdot\cupBq be a partition of the set N of all positive

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IMO 1986 LL CHN15

Origin: CHN

Problem

Let N = B1 \cup\cdot \cdot \cdot\cupBq be a partition of the set N of all positive integers and let an integer l \inN be given. Prove that there exist a set X \subsetN of cardinality l, an infinite set T \subsetN, and an integer k with 1 \leqk \leqq such that for any t \inT and any finite set Y \subsetX, the sum t +  y\inY y belongs to Bk.