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