MathDB

\definecolor{A}{RGB}{70,80,0}\color{A}\fbox{C4.} Show that for any positive integer

n \ge 3

and some subset of

\lbrace{1, 2, . . . , n}\rbrace

with size more than

\frac{n}2 + 1

, there exist three distinct elements

a, b, c

in the subset such that \definecolor{A}{RGB}{255,70,255}\color{A} (ab)^2 + (bc)^2 + (ca)^2is a perfect square.
Proposed by [color=#419DAB]ltf0501. [color=#3D9186]#1736

Problem Statement