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Product set with terms in arithmetic progression !

Source: Romania TST 2015 Day 2 Problem 3

June 4, 2015
arithmetic sequenceSetsProductalgebra

Problem Statement

Given a positive real number tt , determine the sets AA of real numbers containing tt , for which there exists a set BB of real numbers depending on AA , ∣B∣≥4|B| \geq 4 , such that the elements of the set AB={ab∣a∈A,b∈B}AB =\{ ab \mid a\in A , b \in B \} form a finite arithmetic progression .
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