AUSTRIAN-POLISH 2006 Problem 8

Let $A\subset \{x|0\le x<1\}$ with the following properties:

$A$ has at least 4 members.
For all pairwise different $a,b,c,d\in A$ , $ab+cd\in A$ holds. Prove: $A$ has infinetly many members.

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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