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0173 algebra 1st edition Round 7 p3

Source:

May 9, 2021
algebra1st edition

Problem Statement

For a set SS, let ∣S∣|S| denote the number of elements in SS. Let AA be a set of positive integers with ∣A∣=2001|A| = 2001. Prove that there exists a set BB such that all of the following conditions are fulfilled: a) B⊆AB \subseteq A; b) ∣B∣≥668|B| \ge 668; c) for any x,y∈Bx, y \in B we have x+y∉Bx + y \notin B.
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