MathDB

a^2 + b^2 \in A for every a, b \in A with a \ne b

Source: 2011 Romania JBMO TST 3.2

June 1, 2020

Setsalgebra

Problem Statement

Find all the finite sets

A

of real positive numbers having at least two elements, with the property that

a^2 + b^2 \in A

for every

a, b \in A

with

a \ne b