MathDB
A+A ⊃ squares

Source: Brazilian Olympic Revenge 2020, P4

February 1, 2020
olympic revengeBrazilcombinatoricsnumber theoryPerfect SquaresAdditive combinatorics

Problem Statement

Let nn be a positive integer and AA a set of integers such that the set {x=a+b ∣ a,b∈A}\{x = a + b\ |\ a, b \in A\} contains {12,22,…,n2}\{1^2, 2^2, \dots, n^2\}. Prove that there is a positive integer NN such that if n≥Nn \ge N, then ∣A∣>n0.666|A| > n^{0.666}.
Back to ProblemsView on AoPS