MathDB

8

Part of 2006 Austrian-Polish Competition

Problems(1)

Set with infinitely many members

Source: APMC 2006, Problem 8

9/9/2006
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.
inductionabsolute valuealgebra proposedalgebra