MathDB
Pythagorean cycle

Source: Rioplatense L2 2023 #1

December 6, 2023
number theorycombinatorics

Problem Statement

An integer n≥3n\geq 3 is poli-pythagorean if there exist nn positive integers pairwise distinct such that we can order these numbers in the vertices of a regular nn-gon such that the sum of the squares of consecutive vertices is also a perfect square. For instance, 33 is poli-pythagorean, because if we write 44,117,24044,117,240 in the vertices of a triangle we notice: 442+1172=1252,1172+2402=2672,2402+442=244244^2+117^2=125^2, 117^2+240^2=267^2, 240^2+44^2=244^2 Determine all poli-pythagorean integers.
Back to ProblemsView on AoPS