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Set with infinitely many members

Source: APMC 2006, Problem 8

September 9, 2006
inductionabsolute valuealgebra proposedalgebra

Problem Statement

Let A⊂{x∣0≤x<1}A\subset \{x|0\le x<1\} with the following properties: 1. AA has at least 4 members. 2. For all pairwise different a,b,c,d∈Aa,b,c,d\in A, ab+cd∈Aab+cd\in A holds. Prove: AA has infinetly many members.
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