Problem A. 711. (December 2017)
A. 711. For which pairs \(\displaystyle (m,n)\) does there exist an injective function \(\displaystyle f\colon \mathbb{R}^2\to\mathbb{R}^2\) under which the image of every regular \(\displaystyle m\)-gon is a regular \(\displaystyle n\)-gon. (Note that \(\displaystyle m,n\ge 3\), and that by a regular \(\displaystyle N\)-gon we mean the union of the boundary segments, not the closed polygonal region.)
Proposed by: Sutanay Bhattacharya, Bishnupur, India
(5 pont)
Deadline expired on January 10, 2018.
Statistics:
6 students sent a solution. 5 points: Gáspár Attila, Imolay András, Matolcsi Dávid. 4 points: Schrettner Jakab. 3 points: 2 students.
Problems in Mathematics of KöMaL, December 2017