MathDB

C4

Part of 2020-IMOC

Problems(1)

explosive C4 from IMOC - three squares is a square

Source: C4 IMOC 2020

9/5/2020
\definecolor{A}{RGB}{70,80,0}\color{A}\fbox{C4.} Show that for any positive integer n≥3n \ge 3 and some subset of {1,2,...,n}\lbrace{1, 2, . . . , n}\rbrace with size more than n2+1\frac{n}2 + 1, there exist three distinct elements a,b,ca, 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
combinatoricsIMOC