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Set in which each product is a sum

Source: 2023 Israel National Olympiad P6

December 16, 2022
algebraSets

Problem Statement

Determine if there exists a set SS of 57835783 different real numbers with the following property: For every a,b∈Sa,b\in S (not necessarily distinct) there are c≠dc\neq d in SS so that a⋅b=c+da\cdot b=c+d.
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